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@book{BridsonHaeflinger,
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@book{orlik2013arrangements,
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title = {Signed Permutation Statistics and Cycle Type},
journal = {European Journal of Combinatorics},
volume = {14},
number = {6},
pages = {569-579},
year = {1993},
issn = {0195-6698},
doi = {https://doi.org/10.1006/eujc.1993.1059},
url = {https://www.sciencedirect.com/science/article/pii/S0195669883710590},
author = {Victor Reiner},
abstract = {We derive a multivariate generating function which counts signed permutations by their cycle type and to other descent statistics, analogous to a result of Gessel and Reutenauer [4.5] for (unsigned) permutations. The derivation uses a bijection which is the hyperoctahedral analogue of Gessel's necklace bijection.}
}


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author = {Hélène Barcelo}
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@book {Welsh,
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              Thi\'{e}ry, Nicolas M.},
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              theory},
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      YEAR = {2015},
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     PAGES = {169--231},
      ISSN = {0218-1967,1793-6500},
   MRCLASS = {60J10 (05E10 20M30 47D03 60B15 60C05)},
  MRNUMBER = {3325881},
MRREVIEWER = {Michael\ Voit},
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       URL = {https://doi.org/10.1142/S0218196715400081},
}

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  MRNUMBER = {19589},
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@misc{Alexandersson2020,
 author = {Per Alexandersson},
 title = {The symmetric functions catalog},
 howpublished = {Online},
 url = {https://www.symmetricfunctions.com}
} 

@article{Atkinson, author={M. D. Atkinson}, title={Solomon's Descent Algebra Revisited}, journal={Bulletin of the London Mathematical Society}, volume={24}, year={1992}, pages={545-551}}

@misc{brauner2025qdeformedrandomtorandomfamilyhecke,
      title={The $q$-deformed random-to-random family in the {H}ecke algebra}, 
      author={Sarah Brauner and Patricia Commins and Darij Grinberg and Franco Saliola},
      year={2025},
      eprint={2503.17580},
      archivePrefix={arXiv},
      primaryClass={math.CO},
      url={https://arxiv.org/abs/2503.17580}, 
}

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    VOLUME = {10},
      YEAR = {1973},
     PAGES = {177--187},
      ISSN = {0001-8708},
   MRCLASS = {06A50},
  MRNUMBER = {316338},
MRREVIEWER = {Ann\ Miller\ Millman},
       DOI = {10.1016/0001-8708(73)90106-0},
       URL = {https://doi.org/10.1016/0001-8708(73)90106-0},
}

@phdthesis{Uyemura-Reyes, author={J.-C. Uyemura-Reyes}, title={Random Walk, Semi-Direct Products, and Card Shuffling}, year={2002}, school={Stanford University}}

@article{Bergerons-hyper1, author={F. Bergeron and N. Bergeron}, title={A Decomposition of the Descent Algebra of the Hyperoctahedral Group I}, journal={J. Algebra}, year={1992}, volume={148}, pages={86-97}}

@article{Bergerons-hyper2, author={N. Bergeron}, title={A Decomposition of the Descent Algebra of the Hyperoctahedral Group II}, journal={J. Algebra}, year={1992}, volume={148}, pages={98-122}}

@article{stuartmargolist, author={S. Margolis and B. Steinberg}, title={Projective Indecomposable Modules and Quivers for Monoid Algebras}, journal={Communications in Algebra}, year={2018}, volume = {46:12}}

@article{jollenbeckreutenauer, title={Eine Symmetrieeigenschaft von {S}olomons Algebra
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@article{desarmenienwachs, author = {J. D\'{e}sarm\'{e}nien and M. Wachs}, title={Descent Classes of Permutations
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@article{FrenchDesarmenienWachs, 
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 TITLE= {Descentes des d\'{e}rangements et mots circulaires}, 
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JOURNAL={S\'{e}minaire Lotharingien de Combinatoire},
volume={19},
pages={13--21},
URL={https://www.mat.univie.ac.at/~slc/}
}



@article{stanleyhyperplane, author={R. Stanley}, title={An Introduction to Hyperplane Arrangements}, journal={IAS/Park City Mathematics Series}, year={2006}}



@article{Poirier, author={S. Poirier}, title={Cycle Type and Descent Set in Wreath Products}, journal={Discrete Mathematics}, volume={180}, year={1998}, pages={315-343}} 

@article{Bergerons-general, author={F. Bergeron and N. Bergeron and R.B. Howlett and D.E. Taylor}, title={A Decomposition of the Descent Algebra of a Finite {C}oxeter Group}, journal={J. Algebraic Comb.}, year={1992}, volume={1}, pages={23-44}}

@phdthesis{Bidigare,
    title={Hyperplane Arrangement Face Algebras and their Associated {M}arkov Chains},
    author={T. P. Bidigare}, school={University of Michigan},
    year={1997}
}

@book{sagan2013symmetric,
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  author={Sagan, Bruce E},
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  year={2013},
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}

@book{aguiar2006coxeter,
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  year={2006},
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}

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      YEAR = {2015},
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   MRCLASS = {16E30 (05E15 16G10 20M25 52C35)},
  MRNUMBER = {3429159},
MRREVIEWER = {Kenneth\ A.\ Brown},
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  MRNUMBER = {2236757},
MRREVIEWER = {G\"otz\ Pfeiffer},
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       URL = {https://doi-org.srv-proxy1.library.tamu.edu/10.1016/j.jalgebra.2005.07.032},
}

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      ISBN = {0-387-97523-3},
   MRCLASS = {16-01},
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MRREVIEWER = {Gerald J. Janusz},
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title = {The {B}urnside algebra of a finite group},
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number = {4},
pages = {603-615},
year = {1967},
issn = {0021-9800},
doi = {https://doi.org/10.1016/S0021-9800(67)80064-4},
url = {https://www.sciencedirect.com/science/article/pii/S0021980067800644},
author = {Louis Solomon},
abstract = {Let G be a finite group. The isomorphism classes of G-sets generate a commutative ring ℬ[G] which we call the Burnside ring of G. We prove that ℬ[G]⊗Q is a semisimple algebra over Q and that formulas for certain primitive idempotents of this algebra yield the theorem of Artin on rational characters in a explicit form due to Brauer. The proof uses an isomorphism between ℬ[G]⊗Q and an algebra defined by the Möbius function of the partially ordered set of conjugacy classes of subgroups of G.}
}

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volume={24}, 
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volume={58}, 
number={2}
}

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}
}


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@incollection{WachsPosetTopology,
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    volume={96}, 
    number={2}, 
    pages={319 - 341}}

@manual{sagemath,
  Key          = {SageMath},
  Author       = {{The Sage Developers}},
  Title        = {{S}ageMath, the {S}age {M}athematics {S}oftware {S}ystem ({V}ersion 10.1)},
  note         = {{\tt https://www.sagemath.org}},
  Year         = {2024},
}

@article {bonnafepfeiffer,
    AUTHOR = {Bonnaf\'{e}, C. and Pfeiffer, G.},
     TITLE = {Around {S}olomon's descent algebras},
  JOURNAL = {Algebras and Representation Theory},
    VOLUME = {11},
      YEAR = {2008},
    NUMBER = {6},
     PAGES = {577--602},
      ISSN = {1386-923X,1572-9079},
   MRCLASS = {20F55 (05E99)},
  MRNUMBER = {2453230},
MRREVIEWER = {Andrew\ R.\ Francis},
       DOI = {10.1007/s10468-008-9090-9}
}

@incollection {SchockerSurvey,
    AUTHOR = {Schocker, Manfred},
     TITLE = {The descent algebra of the symmetric group},
 BOOKTITLE = {Representations of finite dimensional algebras and related
              topics in {L}ie theory and geometry},
    SERIES = {Fields Inst. Commun.},
    VOLUME = {40},
     PAGES = {145--161},
 PUBLISHER = {American Mathematical Society, Providence, RI},
      YEAR = {2004},
      ISBN = {0-8218-3416-9},
   MRCLASS = {20C30 (17B01 20-02)},
  MRNUMBER = {2057153},
MRREVIEWER = {Christophe\ Hohlweg}
}

@article{DIEKER2018427,
title = {Spectral analysis of random-to-random {M}arkov chains},
journal = {Advances in Mathematics},
volume = {323},
pages = {427-485},
year = {2018},
issn = {0001-8708},
author = {A.B. Dieker and F.V. Saliola},
keywords = {Random-to-random shuffling, Spectrum, Discrete Markov chain, Representation theory, Symmetric group},
abstract = {We compute the eigenvalues and eigenspaces of random-to-random Markov chains. We use a family of maps which reveal a remarkable recursive structure of the eigenspaces, yielding an explicit and effective construction of all eigenbases starting from bases of the kernels.}
}




@article{Albach-Swanson,
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  author={Ahlbach, Connor and Swanson, Joshua P},
  journal={The Electronic Journal of Combinatorics},
  pages={4-42},
  year={2018}
}

@article{pfeiffer2009quiver,
  title={A quiver presentation for {S}olomon's descent algebra},
  author={Pfeiffer, G{\"o}tz},
  journal={Advances in Mathematics},
  volume={220},
  number={5},
  pages={1428--1465},
  year={2009},
  publisher={Elsevier}
}

 @article {BHR,
    AUTHOR = {Bidigare, Pat and Hanlon, Phil and Rockmore, Dan},
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   MRCLASS = {52C35 (15A18)},
  MRNUMBER = {1700744},
MRREVIEWER = {Hiroaki\ Terao},
       DOI = {10.1215/S0012-7094-99-09906-4},
       URL = {https://doi-org.srv-proxy1.library.tamu.edu/10.1215/S0012-7094-99-09906-4},
}
   
    
@article{browndiac, 
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}
@book{webbrepntheory, author = {Webb, Peter}, year={2016}, title={A Course in Finite Group Representation Theory}, publisher={Cambridge University Press}}

@article{saliolaquiverlrb, 
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      YEAR = {2007},
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  MRNUMBER = {2378054},
MRREVIEWER = {XianKun\ Du},
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}

@article{saliolaquiverdescalgebra,
    AUTHOR = {Saliola, Franco V.},
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      YEAR = {2008},
    NUMBER = {11},
     PAGES = {3866--3894},
      ISSN = {0021-8693,1090-266X},
   MRCLASS = {20F55 (16G20)},
  MRNUMBER = {2464797},
MRREVIEWER = {Rafael\ Stekolshchik},
       DOI = {10.1016/j.jalgebra.2008.07.009},
       URL = {https://doi-org.srv-proxy1.library.tamu.edu/10.1016/j.jalgebra.2008.07.009},
}

@phdthesis{lafreniere,
    author ={Nadia Lafreni\`{e}re} ,
    title = {Valeurs propres des op\'{e}rateurs de m\'{e}langes sym\'{e}tris\'{e}s},
    school ={Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al },
    year ={2019}
}

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@book{tits1974buildings,
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}

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 publisher = {Annals of Mathematics},
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}



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}

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@misc{bastidas-talk, author={J. Bastidas}, title={The polytope algebra of generalized permutahedra}, year={2020}, month={Sep. 30}, note={Talk at Graduate Online Combinatorics Colloquium}}

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@article{SpeyerSturmfels,
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}

@article{Buneman,
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pages={387-395},
    year ={1971}
}

@article{Schroder,
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}

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}

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  MRNUMBER = {4554674},
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       URL = {https://doi.org/10.1016/j.aam.2023.102502},
}

@article {Chepoi,
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    VOLUME = {24},
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   MRCLASS = {57M07 (05C10 20F67)},
  MRNUMBER = {1748966},
       DOI = {10.1006/aama.1999.0677},
       URL = {https://doi.org/10.1006/aama.1999.0677},
}

@article{Bandelt-Hans-Juergen-Chepoi,
    AUTHOR = {Bandelt, Hans-J\"urgen and Chepoi, Victor and Knauer, Kolja},
     TITLE = {C{OM}s: complexes of oriented matroids},
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  FJOURNAL = {Journal of Combinatorial Theory. Series A},
    VOLUME = {156},
      YEAR = {2018},
     PAGES = {195--237},
      ISSN = {0097-3165,1096-0899},
   MRCLASS = {52C40 (05B35)},
  MRNUMBER = {3762108},
MRREVIEWER = {Steven\ N.\ Karp},
       DOI = {10.1016/j.jcta.2018.01.002},
       URL = {https://doi-org.srv-proxy1.library.tamu.edu/10.1016/j.jcta.2018.01.002},
}

@article{BillerHolmesVogtmann,
title = {Geometry of the Space of Phylogenetic Trees},
journal = {Advances in Applied Mathematics},
volume = {27},
number = {4},
pages = {733-767},
year = {2001},
issn = {0196-8858},
doi = {https://doi.org/10.1006/aama.2001.0759},
url = {https://www.sciencedirect.com/science/article/pii/S0196885801907596},
author = {Louis J. Billera and Susan P. Holmes and Karen Vogtmann},
}


@book{etingof, author={P. Etingof and O. Golberg and S.
Hensel and T. Liu and A. Schwendner and
D. Vaintrob and E. Yudovina
and S.
Gerovitch}, title={Introduction to Representation Theory}, year={2011}, publisher={AMS Student Mathematical Library, 59}}

@book{assem, title={Elements of the Representation Theory of Associative Algebras Volume I}, author={I. Assem and D. Simson and A. Skowro\'{n}ski}, publisher={Cambridge University Press}, year={2006}}

@article{sundaramwelker,
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@article{mantacireutenauerbonnafehohlweg, author = {C. Bonnaf\'{e} and C. Hohlweg}, title={Generalized Descent Algebra
and Construction of Irreducible Characters of Hyperoctahedral group}, journal={Annales de l'Institut Fourier}, volume={ 56:1}, year={2006}, pages={131-181}}

@book{reutenauer, 
author={Christophe Reutenauer}, 
title={Free {L}ie Algebras}, 
year={1993}, 
volume={7}, 
note={London Mathematical Society Monographs, New Series},
publisher={Oxford University Press}
}

@article{BraunerComminsReiner,
  doi = {10.2140/pjm.2023.322.251},
  
  author = {Brauner, Sarah and Commins, Patricia and Reiner, Victor},
  
  title = {Invariant theory for the free left-regular band and a $q
  $-analogue},
  
  journal = {Pacific J. Math.},
  
  year = {2023},
 volume={322}, 
 number={2},
 pages={251-280}
}

@book{LundellWeingram, title={The Topology of $CW$ Complexes}, author={Lundell, A. and Weingram, S.}, year={1969}, publisher={Van Nostrand Reinhold Company}}

@article{bjorner, author={Bj\"{o}rner, A.}, title={Posets, Regular {CW} Complexes and {B}ruhat Order}, journal={European Journal of Combinatorics}, year={1984}, volume={5}, pages={7 - 16}}

@misc{BastidasBraunerSaliola,
      title={Left Regular Bands of Groups and the {M}antaci--{R}eutenauer algebra}, 
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      year={2023},
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      archivePrefix={arXiv},
      primaryClass={math.CO}
}

@article{CoxeterCAT0,
author={G.A. Niblo and L.D. Reeves},
url = {https://doi.org/10.1515/jgth.2003.028},
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pages = {399--413},
volume = {6},
number = {3},
journal = {Journal of Group Theory},
doi = {doi:10.1515/jgth.2003.028},
year = {2003},
lastchecked = {2023-06-28}
}


@article {ArdilaSociety,
    AUTHOR = {Ardila-Mantilla, Federico},
     TITLE = {{$\rm CAT(0)$} geometry, robots, and society},
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    VOLUME = {67},
      YEAR = {2020},
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     PAGES = {977--987},
      ISSN = {0002-9920,1088-9477},
   MRCLASS = {05C10 (57Q05 68T40)},
  MRNUMBER = {4187094},
       DOI = {10.1090/noti},
       URL = {https://doi.org/10.1090/noti},
}

@article {ArdilaBakerYatchak,
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     TITLE = {Moving robots efficiently using the combinatorics of {CAT}(0)
              cubical complexes},
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   MRCLASS = {68T40 (05A15 06A07 53C23 57Q05)},
  MRNUMBER = {3224575},
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       URL = {https://doi.org/10.1137/120898115},
}

@article {NibloReevesOlder,
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    VOLUME = {37},
      YEAR = {1998},
    NUMBER = {3},
     PAGES = {621--633},
      ISSN = {0040-9383},
   MRCLASS = {20F32 (20F55 57M50)},
  MRNUMBER = {1604899},
MRREVIEWER = {Darryl\ McCullough},
       DOI = {10.1016/S0040-9383(97)00018-9},
       URL = {https://doi.org/10.1016/S0040-9383(97)00018-9},
}


@article {SteinbergMonoidTopology,
    AUTHOR = {Steinberg, Benjamin},
     TITLE = {Topology and monoid representations {I}: {F}oundations},
   JOURNAL = {J. Pure Appl. Algebra},
  FJOURNAL = {Journal of Pure and Applied Algebra},
    VOLUME = {229},
      YEAR = {2025},
    NUMBER = {1},
     PAGES = {Paper No. 107848, 36},
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   MRCLASS = {20M25 (05E10 05E45 16G99 20M30 20M50)},
  MRNUMBER = {4837173},
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       URL = {https://doi.org/10.1016/j.jpaa.2024.107848},
}

@book{SteinbergRepMonoidsBook,
author = {Steinberg, Benjamin},
year = {2016},

title = {Representation Theory of Finite Monoids},
publisher={Springer}
}

@article{Ardila-Klivans,
author = {Ardila, Federico and Klivans, Caroline},
year = {2003},
month = {12},
pages = {38-49},
title = {The {B}ergman complex of a matroid and phylogenetic trees},
volume = {96},
journal = {Journal of Combinatorial Theory, Series B},
doi = {10.1016/j.jctb.2005.06.004}
}

@ARTICLE{Owen-Provan,
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  journal={IEEE/ACM Transactions on Computational Biology and Bioinformatics}, 
  title={A Fast Algorithm for Computing Geodesic Distances in Tree Space}, 
  year={2011},
  volume={8},
  number={1},
  pages={2-13},
  doi={10.1109/TCBB.2010.3}}

@article{StanleyRelativeInvariants,
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    journal = {Journal of Algebra},
volume={49},
    year = 1977,
pages={134-148}
}

@article{Ardila-Owen-Sullivant,
title = {Geodesics in {CAT}(0) cubical complexes},
author={Federico Ardila and Megan Owen and Seth Sullivant},
journal = {Advances in Applied Mathematics},
volume = {48},
number = {1},
pages = {142-163},
year = {2012},
issn = {0196-8858},
doi = {https://doi.org/10.1016/j.aam.2011.06.004},
url = {https://www.sciencedirect.com/science/article/pii/S0196885811000613}
}

@article{Miller-Owen-Provan,
title = {Polyhedral computational geometry for averaging metric phylogenetic trees},
journal = {Advances in Applied Mathematics},
volume = {68},
pages = {51-91},
year = {2015},
issn = {0196-8858},
doi = {https://doi.org/10.1016/j.aam.2015.04.002},
url = {https://www.sciencedirect.com/science/article/pii/S0196885815000470},
author = {Ezra Miller and Megan Owen and J. Scott Provan}
}

%For Whitehouse Simplicial Complex:
@incollection {Boardman,
    AUTHOR = {Boardman, J. M.},
     TITLE = {Homotopy structures and the language of trees},
 BOOKTITLE = {Algebraic topology ({P}roc. {S}ympos. {P}ure {M}ath., {V}ol.
              {XXII}, {U}niv. {W}isconsin, {M}adison, {W}is., 1970)},
     PAGES = {pp 37--58},
 PUBLISHER = {Amer. Math. Soc., Providence, R.I.},
      YEAR = {1971},
   MRCLASS = {55D35},
  MRNUMBER = {350723},
MRREVIEWER = {J.\ Stasheff},
}
@article{CullerVogtmann,
  title={Moduli of graphs and automorphisms of free groups},
  author={Marc Culler and Karen Vogtmann},
  journal={Inventiones mathematicae},
  year={1986},
  volume={84},
  pages={91-119},
  url={https://api.semanticscholar.org/CorpusID:122869546}
}


@phdthesis{Whitehouse,
    author = {Sarah Whitehouse},
    title = {Gamma (co)homology of commutative algebras and some related representations of the symmetric group},
    school = {University of Warwick},
    year = {1994}
}

@article {Readdy,
    AUTHOR = {Readdy, Margaret A.},
     TITLE = {The pre-{WDVV} ring of physics and its topology},
   JOURNAL = {Ramanujan J.},
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              Areas of Mathematics Influenced by Ramanujan},
    VOLUME = {10},
      YEAR = {2005},
    NUMBER = {2},
     PAGES = {269--281},
      ISSN = {1382-4090,1572-9303},
   MRCLASS = {13F55 (05E99 55P15)},
  MRNUMBER = {2195566},
MRREVIEWER = {Anargyros\ Katsabekis},
       DOI = {10.1007/s11139-005-4850-1},
       URL = {https://doi.org/10.1007/s11139-005-4850-1},
}

@article {Robinson-Whitehouse,
    AUTHOR = {Robinson, Alan and Whitehouse, Sarah},
     TITLE = {The tree representation of {$\Sigma_{n+1}$}},
   JOURNAL = {J. Pure Appl. Algebra},
  FJOURNAL = {Journal of Pure and Applied Algebra},
    VOLUME = {111},
      YEAR = {1996},
    NUMBER = {1-3},
     PAGES = {245--253},
      ISSN = {0022-4049,1873-1376},
   MRCLASS = {55P15 (17B01)},
  MRNUMBER = {1394355},
MRREVIEWER = {Alexander\ I.\ Barvinok},
       DOI = {10.1016/0022-4049(95)00116-6},
       URL = {https://doi.org/10.1016/0022-4049(95)00116-6},
}

@article {SundaramNonModular,
    AUTHOR = {Sundaram, Sheila},
     TITLE = {Homotopy of non-modular partitions and the {W}hitehouse
              module},
   JOURNAL = {J. Algebraic Combin.},
  FJOURNAL = {Journal of Algebraic Combinatorics. An International Journal},
    VOLUME = {9},
      YEAR = {1999},
    NUMBER = {3},
     PAGES = {251--269},
      ISSN = {0925-9899,1572-9192},
   MRCLASS = {05E25 (06A11 20C30)},
  MRNUMBER = {1695076},
MRREVIEWER = {Eva-Maria\ E.\ Feichtner},
       DOI = {10.1023/A:1018648219348},
       URL = {https://doi.org/10.1023/A:1018648219348},
}

@article {Vogtmann,
    AUTHOR = {Vogtmann, Karen},
     TITLE = {Local structure of some {${\rm Out}(F_n)$}-complexes},
   JOURNAL = {Proc. Edinburgh Math. Soc. (2)},
  FJOURNAL = {Proceedings of the Edinburgh Mathematical Society. Series II},
    VOLUME = {33},
      YEAR = {1990},
    NUMBER = {3},
     PAGES = {367--379},
      ISSN = {0013-0915,1464-3839},
   MRCLASS = {57M07 (20F28)},
  MRNUMBER = {1077791},
MRREVIEWER = {Ruth\ Charney},
       DOI = {10.1017/S0013091500004818},
       URL = {https://doi.org/10.1017/S0013091500004818},
}

@article {Trappmann-Ziegler,
    AUTHOR = {Trappmann, Henryk and Ziegler, G\"{u}nter M.},
     TITLE = {Shellability of complexes of trees},
   JOURNAL = {J. Combin. Theory Ser. A},
  FJOURNAL = {Journal of Combinatorial Theory. Series A},
    VOLUME = {82},
      YEAR = {1998},
    NUMBER = {2},
     PAGES = {168--178},
      ISSN = {0097-3165,1096-0899},
   MRCLASS = {05E25 (05C05 57M15)},
  MRNUMBER = {1620865},
MRREVIEWER = {Volker\ Strehl},
       DOI = {10.1006/jcta.1997.2844},
       URL = {https://doi.org/10.1006/jcta.1997.2844},
}

@article{EarlyReiner,
title = {On configuration spaces and {W}hitehouse's lifts of the {E}ulerian representations},
journal = {Journal of Pure and Applied Algebra},
volume = {223},
number = {10},
pages = {4524-4535},
year = {2019},
issn = {0022-4049},
doi = {https://doi.org/10.1016/j.jpaa.2019.02.002},
url = {https://www.sciencedirect.com/science/article/pii/S0022404919300362},
author = {Nicholas Early and Victor Reiner},
abstract = {S. Whitehouse's lifts of the Eulerian representations of Sn to Sn+1 are reinterpreted, topologically and ring-theoretically, building on the first author's work on A. Ocneanu's theory of permutohedral blades.}
}
@ARTICLE{Brauner2022,
	author = {Brauner, Sarah},
	title = {Eulerian representations for real reflection groups},
	year = {2022},
	journal = {Journal of the London Mathematical Society},
	volume = {105},
	number = {1},
pages={412-444}
}

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@article{schocker2003multiplicities,
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@book{OrientedMatroids, 
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DOI={10.1017/CBO9780511586507}, publisher={Cambridge University Press}, 
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collection={Encyclopedia of Mathematics and its Applications}}

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       URL = {https://doi.org/10.1016/j.jalgebra.2024.10.041},
}

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MRREVIEWER = {Toufik Mansour},
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}

@article {HershReiner,
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}

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@article{SundaramWhitehouseTwo,
title = {On the topology of two partition posets with forbidden block sizes},
journal = {Journal of Pure and Applied Algebra},
volume = {155},
number = {2},
pages = {271-304},
year = {2001},
issn = {0022-4049},
doi = {https://doi.org/10.1016/S0022-4049(99)00090-0},
url = {https://www.sciencedirect.com/science/article/pii/S0022404999000900},
author = {Sheila Sundaram},
abstract = {We study two subposets of the partition lattice obtained by restricting block sizes. The first consists of set partitions of {1,…,n} with block size at most k, for k≤n−2. We show that the order complex has the homotopy type of a wedge of spheres, in the cases 2k+2≥n and n=3k+2. For 2k+2>n, the posets in fact have the same Sn−1-homotopy type as the order complex of Πn−1, and the Sn-homology representation is the “tree representation” of Robinson and Whitehouse. We present similar results for the subposet of Πn in which a unique block size k≥3 is forbidden. For 2k≥n, the order complex has the homotopy type of a wedge of (n−4)-spheres. The homology representation of Sn can be simply described in terms of the Whitehouse lifting of the homology representation of Πn−1.}
}

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@phdthesis{ComminsThesis,
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    title = {Left regular bands with symmetry},
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    year = {2025}
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@article{commins2024invariant,
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MRREVIEWER = {Ellen\ E.\ Kirkman},
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       URL = {https://doi-org.srv-proxy1.library.tamu.edu/10.5802/alco.412},
}


@article{ALCO_2019__2_4_613_0,
     author = {Proudfoot, Nicholas},
     title = {Equivariant {Kazhdan{\textendash}Lusztig} polynomials of $q$-niform matroids},
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     publisher = {MathOA foundation},
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     number = {4},
     year = {2019},
     doi = {10.5802/alco.59},
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     mrnumber = {3997514},
     language = {en},
     url = {https://alco.centre-mersenne.org/articles/10.5802/alco.59/}
}


@ARTICLE{Brauner2023,
	author = {Brauner, Sarah},
	title = {A Type {B} analog of the {W}hitehouse representation},
	year = {2023},
	journal = {Mathematische Zeitschrift},
	volume = {303},
	number = {3},
	doi = {10.1007/s00209-022-03200-7},
	url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85148106949&doi=10.1007%2fs00209-022-03200-7&partnerID=40&md5=045c325b3aa6143404d72d916b88c3c6}
}



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