% This is an example bibliography file for FPSAC submissions. @article{greenwade93, author = {George D. Greenwade}, date-modified = {2016-08-11 21:04:25 +0000}, journal = {TUGBoat}, number = {3}, pages = {342--351}, title = {The {C}omprehensive {T}ex {A}rchive {N}etwork ({CTAN})}, url = {https://www.google.com}, volume = {14}, year = {1993}, bdsk-url-1 = {https://www.google.com} } @misc{ellisset, title={Setwise intersecting families of permutations}, author={David Ellis}, year={2019}, eprint={1106.0725}, archivePrefix={arXiv}, primaryClass={math.CO}, url={https://arxiv.org/abs/1106.0725}, } @article{MR4, author = {Corliss, J. J.}, title = {Upper limits to the real roots of a real algebraic equation}, journal = {Amer. Math. Monthly}, fjournal = {The American Mathematical Monthly}, volume = {46}, year = {1939}, pages = {334--338}, issn = {0002-9890}, mrclass = {09.0X}, mrnumber = {0000004}, mrreviewer = {O. Sz\'asz}, doi = {10.2307/2302887} } @article{ErdosT67b, title={On Some Problems of a Statistical Group-Theory. II}, author={Paul Erd{\H{o}}s and Paul Tur{\'a}n}, journal={Acta Mathematica Academiae Scientiarum Hungarica}, year={1967}, volume={18}, pages={151-163}, url={https://api.semanticscholar.org/CorpusID:14377503} } @article{SiemonsZ19, title = "Remarks on singular Cayley graphs and vanishing elements of simple groups", abstract = "Let Γ be a finite graph and let A(Γ) be its adjacency matrix. Then Γ is singular if A(Γ) is singular. The singularity of graphs is of certain interest in graph theory and algebraic combinatorics. Here we investigate this problem for Cayley graphs Cay(G,H) when G is a finite group and when the connecting set H is a union of conjugacy classes of G. In this situation, the singularity problem reduces to finding an irreducible character χ of G for which ∑h∈Hχ(h)=0. At this stage, we focus on the case when H is a single conjugacy class hG of G; in this case, the above equality is equivalent to χ(h)=0 . Much is known in this situation, with essential information coming from the block theory of representations of finite groups. An element h∈G is called vanishing if χ(h)=0 for some irreducible character χ of G. We study vanishing elements mainly in finite simple groups and in alternating groups in particular. We suggest some approaches for constructing singular Cayley graphs.", keywords = "Singular Cayley graphs, Vertex transitive graphs, Vanishing elements, Block theory of symmetric and alternating groups", author = "Johannes Siemons and Alexandre Zalesski", year = "2019", doi = "10.1007/s10801-018-0860-0", language = "English", volume = "50", pages = "379--401", journal = "Journal of Algebraic Combinatorics", issn = "0925-9899", publisher = "Springer", number = "4", } @article{Renteln25, title = {Counting Sylow double cosets in the symmetric group}, journal = {Discrete Mathematics}, volume = {347}, number = {10}, pages = {114109}, year = {2024}, issn = {0012-365X}, doi = {https://doi.org/10.1016/j.disc.2024.114109}, url = {https://www.sciencedirect.com/science/article/pii/S0012365X24002401}, author = {Paul Renteln}, keywords = {Symmetric group, Sylow--subgroup, Double cosets, Cycle index, Wreath product}, abstract = {An algorithm is developed for calculating the number of double cosets P﹨Sn/P, where P is a Sylow-p-subgroup of the symmetric group Sn. Several examples of its use are given.} } @article{lovasz, title={On the {Shannon} capacity of a graph}, author={Lov{\'a}sz, L{\'a}szl{\'o}}, journal={IEEE Transactions on Information Theory}, volume={25}, number={1}, pages={1--7}, year={1979}, publisher={IEEE}, doi={10.1109/TIT.1979.1055985} } @article{lindzey, title={An {E}ventown {R}esult for {P}ermutations}, author={Lindzey, Nathan}, journal={arXiv preprint arXiv:2601.12613}, year={2026}, url={https://arxiv.org/abs/2601.12613} } @article{StaceyO23, author = {Law, Stacey and Okitani, Yuji}, title = {On plethysms and {Sylow} branching coefficients}, journal = {Algebraic Combinatorics}, pages = {321--357}, year = {2023}, publisher = {The Combinatorics Consortium}, volume = {6}, number = {2}, doi = {10.5802/alco.262}, language = {en}, url = {https://alco.centre-mersenne.org/articles/10.5802/alco.262/} } @article{Chen24, author = {Chen, William Y.C.}, journal = {Enumerative combinatorics and applications}, number = {3}, organization = {Tianjin University}, publisher = {University of Haifa, Department of Mathematics}, title = {Breaking cycles, the odd versus the even}, volume = {4}, year = {2024}, } @phdthesis{Kapadia25, author = {Zain Ahmed Kapadia}, title = {On the Submodule Structure of Hook Specht Modules in Characteristic 2}, school = {Queen Mary University of London}, year = {2025} } @article{Murphy82, title = {Submodule structure of some Specht modules}, journal = {Journal of Algebra}, volume = {74}, number = {2}, pages = {524-534}, year = {1982}, issn = {0021-8693}, doi = {https://doi.org/10.1016/0021-8693(82)90038-2}, url = {https://www.sciencedirect.com/science/article/pii/0021869382900382}, author = {Gwendolen Murphy} } @article{Peel71, title={Hook representations of the symmetric groups}, volume={12}, DOI={10.1017/S0017089500001245}, number={2}, journal={Glasgow Mathematical Journal}, publisher={Cambridge University Press}, author={Peel, M. H.}, year={1971}, pages={136–149}} @book{GodsilMeagher, title={Erd{\H{o}}s--Ko--Rado Theorems: Algebraic Approaches}, author={Godsil, C. and Meagher, K.}, isbn={9781107128446}, series={Cambridge Studies in Advanced Mathematics}, url={https://books.google.ca/books?id=P0XjCgAAQBAJ}, year={2015}, publisher={Cambridge University Press} } @article{Giannelli17, author = {Giannelli, Eugenio}, title = {Characters of odd degree of symmetric groups}, journal = {Journal of the London Mathematical Society}, volume = {96}, number = {1}, pages = {1-14}, keywords = {20C30 (primary), 20C15 (secondary)}, doi = {https://doi.org/10.1112/jlms.12048}, url = {https://londmathsoc.onlinelibrary.wiley.com/doi/abs/10.1112/jlms.12048}, abstract = {Abstract We construct a natural bijection between odd-degree irreducible characters of S2n and linear characters of its Sylow 2-subgroup P2n. We show that such a bijection is nicely induced by the restriction functor. We conclude with a characterization of the irreducible characters χ of Sn such that the restriction of χ to Pn has a unique linear constituent.}, year = {2017} } @article{DiaconisGGLNSS25, title = {On the number and sizes of double cosets of Sylow subgroups of the symmetric group}, journal = {Journal of Algebra}, volume = {689}, pages = {62-86}, year = {2026}, issn = {0021-8693}, doi = {https://doi.org/10.1016/j.jalgebra.2025.09.036}, url = {https://www.sciencedirect.com/science/article/pii/S0021869325005824}, author = {Persi Diaconis and Eugenio Giannelli and Robert M. Guralnick and Stacey Law and Gabriel Navarro and Benjamin Sambale and Hunter Spink}, keywords = {Symmetric groups, Sylow subgroups, Double cosets}, abstract = {Let Pn be a Sylow p-subgroup of the symmetric group Sn. We investigate the number and sizes of the Pn∖Sn/Pn double cosets, showing that ‘most’ double cosets have maximal size when p is odd, or equivalently, that Pn∩Pnx=1 for most x∈Sn when n is large. We also find that all possible sizes of such double cosets occur, modulo a list of small exceptions.} } @article{MalleZ20, url = {https://doi.org/10.1515/jgth-2019-0024}, title = {Steinberg-like characters for finite simple groups}, author = {Gunter Malle and Alexandre Zalesski}, pages = {25--78}, volume = {23}, number = {1}, journal = {Journal of Group Theory}, doi = {doi:10.1515/jgth-2019-0024}, year = {2020}, lastchecked = {2025-04-25} } @article{Taylor17, title = {A note on skew characters of symmetric groups}, author = {Jay Taylor}, pages = {435--43}, volume = {221}, journal = {Israel Journal of Mathematics}, year = {2017}, } @article{Regev13, title = "Lie superalgebras and some characters of $S_n$", abstract = "We prove a formula for S n characters which are indexed by the partitions in the (k, ℓ) hook. The proof applies a combinatorial part of the theory of Lie superalgebras [1].", author = "Amitai Regev", year = "2013", doi = "10.1007/s11856-012-0095-z", language = "English", volume = "195", pages = "31--35", journal = "Israel Journal of Mathematics", issn = "0021-2172", publisher = "Springer New York", number = "1", } @article{Ebrahimi26, title = {Singular Cayley graphs and $p$-blocks of finite groups}, journal = {Journal of Algebra}, volume = {687}, pages = {477-491}, year = {2026}, issn = {0021-8693}, doi = {https://doi.org/10.1016/j.jalgebra.2025.08.038}, url = {https://www.sciencedirect.com/science/article/pii/S0021869325005241}, author = {Mahdi Ebrahimi}, keywords = {Cayley graph, -block, Singular graph, Nullity, Energy}, abstract = {For a simple finite graph Γ, the multiplicity of the eigenvalue 0 of the adjacency matrix of Γ is called the nullity of Γ. The energy of Γ is defined as the sum of the absolute values of its eigenvalues. In this paper, we apply the block theory of finite groups to study the Cayley graph Γp(G) defined on a finite group G in which its connecting set consists of p-singular elements of G. We use this Cayley graph to investigate several methods for constructing singular graphs. Then we assume that G is p-solvable and obtain some nice restrictions on the structure of Γp(G). We first achieve an explicit formula for the nullity of Γp(G). In addition, we find a lower bound for the energy of Γp(G). Finally, we prove that the diameter of Γp(G) is at most |G|p.} } @MISC {HopkinsMO, TITLE = {A bijection on permutations}, AUTHOR = {Sam Hopkins}, HOWPUBLISHED = {MathOverflow}, NOTE = {(version: 2021-12-29)}, URL = {https://mathoverflow.net/q/412731} } @article{Eberhard25, url = {https://doi.org/10.1515/jgth-2025-0094}, title = {Intersections of Sylow 2-subgroups in symmetric groups}, author = {Sean Eberhard}, journal = {Journal of Group Theory}, doi = {doi:10.1515/jgth-2025-0094}, year = {Accepted for publication}, lastchecked = {2025-11-03} } @article{Berlekamp69, title={On Subsets with Intersections of Even Cardinality}, volume={12}, DOI={10.4153/CMB-1969-059-3}, number={4}, journal={Canadian Mathematical Bulletin}, author={Berlekamp, E.R.}, year={1969}, pages={471–474}}
@article{ErnstS23, title={Intersection theorems for finite general linear groups}, volume={175}, DOI={10.1017/S0305004123000075}, number={1}, journal={Mathematical Proceedings of the Cambridge Philosophical Society}, author={Ernst, Alena and Schmidt, Kai-Uwe}, year={2023}, pages={129–160}} @book{BF92, author = {Babai, L. and Frankl, P.}, title = {Linear algebra methods in combinatorics with applications to geometry and computer science}, year = {1992}, publisher = {The University of Chicago} } @article{KellerLMS24, title = {On t-intersecting families of permutations}, journal = {Advances in Mathematics}, volume = {445}, pages = {109650}, year = {2024}, issn = {0001-8708}, doi = {https://doi.org/10.1016/j.aim.2024.109650}, url = {https://www.sciencedirect.com/science/article/pii/S0001870824001658}, author = {Nathan Keller and Noam Lifshitz and Dor Minzer and Ohad Sheinfeld}, keywords = {Intersection problems, Erdős-Ko-Rado, Permutations, Hypercontractivity for global functions, Ahlswede-Khachatrian, Forbidden intersection, -intersecting}, abstract = {We prove that there exists a constant c0 such that for any t∈N and any n≥c0t, if A⊂Sn is a t-intersecting family of permutations then |A|≤(n−t)!. Furthermore, if |A|≥0.75(n−t)! then there exist i1,…,it and j1,…,jt such that σ(i1)=j1,…,σ(it)=jt holds for any σ∈A. This shows that the conjectures of Deza and Frankl (1977) and of Cameron (1988) on t-intersecting families of permutations hold for all t≤c0n. Our proof method, based on hypercontractivity for global functions, does not use the specific structure of permutations, and applies in general to t-intersecting sub-families of ‘pseudorandom’ families in {1,2,…,n}n, like Sn.} } @article{KupavskiiZ24, title = {Spread approximations for forbidden intersections problems}, journal = {Advances in Mathematics}, volume = {445}, pages = {109653}, year = {2024}, issn = {0001-8708}, doi = {https://doi.org/10.1016/j.aim.2024.109653}, url = {https://www.sciencedirect.com/science/article/pii/S0001870824001683}, author = {Andrey Kupavskii and Dmitrii Zakharov}, keywords = {Intersecting family, Spread approximation, Extremal set theory, Erdos-Ko-Rado}, abstract = {We develop a new approach to approximate families of sets, complementing the existing ‘Δ-system method’ and ‘junta approximations method’. The approach, which we refer to as ‘spread approximations method’, is based on the notion of r-spread families and builds on the recent breakthrough result of Alweiss, Lovett, Wu and Zhang for the Erdős–Rado ‘Sunflower Conjecture’. Our approach can work in a variety of sparse settings. To demonstrate the versatility and strength of the approach, we present several of its applications to forbidden intersection problems, including bounds on the size of regular intersecting families, the resolution of the Erdős–Sós problem for sets in a new range and, most notably, the resolution of the t-intersection and Erdős–Sós problems for permutations in a new range. Specifically, we show that any collection of permutations of an n-element set with no two permutations intersecting in at most (exactly) t−1 elements has size at most (n−t)!, provided t⩽n1−ϵ (t⩽n13−ϵ) for an arbitrary ϵ>0 and n>n0(ϵ). Previous results for these problems only dealt with the case of fixed t. The proof follows the structure vs. randomness philosophy, which proved to be very efficient in proving results throughout mathematics and computer science.} } @article{DafniFLLV26, author = {Neta Dafni and Yuval Filmus and Noam Lifshitz and Nathan Lindzey and Marc Vinyals}, title = {Complexity Measures on the Symmetric Group and Beyond}, journal = {Combinatorial Theory}, year = {2026}, note = {Accepted for publication.} } @article{Ellis12, title = {Setwise intersecting families of permutations}, journal = {Journal of Combinatorial Theory, Series A}, volume = {119}, number = {4}, pages = {825-849}, year = {2012}, issn = {0097-3165}, doi = {https://doi.org/10.1016/j.jcta.2011.12.003}, url = {https://www.sciencedirect.com/science/article/pii/S0097316511001920}, author = {David Ellis}, keywords = {Intersecting families of permutations, Erdős–Ko–Rado, Representation theory}, abstract = {A family of permutations A⊂Sn is said to be t-set-intersecting if for any two permutations σ,π∈A, there exists a t-set x whose image is the same under both permutations, i.e. σ(x)=π(x). We prove that if n is sufficiently large depending on t, the maximum-sized t-set-intersecting families of permutations in Sn are cosets of stabilizers of t-sets. The t=2 case of this was conjectured by János Körner. It can be seen as a variant of the Deza–Frankl conjecture, proved in Ellis, Friedgut and Pilpel (2011) [3]. Our proof uses similar techniques to those of Ellis, Friedgut and Pilpel (2011) [3], namely, eigenvalue methods, together with the representation theory of the symmetric group, but the combinatorial part of the proof is harder.} } @article{EllisFP11, author = {D. Ellis and E. Friedgut and H. Pilpel}, title = {Intersecting families of permutations}, journal = {Journal of the American Mathematical Society}, volume = {24}, year = {2011}, pages = {649-682} } @article{KuLW16, author = {Ku, Cheng Yeaw and Lau, Terry and Wong, Kok Bin}, title = {Largest independent sets of certain regular subgraphs of the derangement graph}, year = {2016}, issue_date = {August 2016}, publisher = {Kluwer Academic Publishers}, address = {USA}, volume = {44}, number = {1}, issn = {0925-9899}, url = {https://doi.org/10.1007/s10801-015-0656-4}, doi = {10.1007/s10801-015-0656-4}, abstract = {The derangement graph is the Cayley graph on the symmetric group $$mathcal {S}_{n}$$Sn whose generating set $$D_{n}$$Dn is the set of permutations on $$[n]={1, ldots , n}$$[n]={1,\'{z},n} without any 1-cycle. For any fixed positive integer $$k le n$$k≤n, the Cayley graph generated by the subset of $$D_{n}$$Dn consisting of permutations without any i-cycles for all $$1 le i le k$$1≤i≤k is a regular subgraph of the derangement graph. In this paper, we determine the smallest eigenvalue of these subgraphs and show that the set of all the largest independent sets in these subgraphs is equal to the set of all the largest independent sets in the derangement graph, provided n is sufficiently large in terms of k.}, journal = {Journal of Algebraic Combinatorics}, pages = {81–98}, numpages = {18} } @article{FilmusL24, author = {Filmus, Yuval and Lindzey, Nathan}, title = {A note on “Largest independent sets of certain regular subgraphs of the derangement graph”}, year = {2024}, issue_date = {May 2024}, publisher = {Kluwer Academic Publishers}, address = {USA}, volume = {59}, number = {3}, issn = {0925-9899}, url = {https://doi.org/10.1007/s10801-024-01304-3}, doi = {10.1007/s10801-024-01304-3}, abstract = {Let Dn,k be the set of all permutations of the symmetric group Sn that have no cycles of length i for all 1≤i≤k. In the paper mentioned above, Ku, Lau, and Wong prove that the set of all the largest independent sets of the Cayley graph Cay(Sn,Dn,k) is equal to the set of all the largest independent sets in the derangement graph Cay(Sn,Dn,1), provided n is sufficiently large in terms of k. We give a simpler proof that holds for all n, k and also applies to the alternating group.}, journal = {Journal of Algebraic Combinatorics}, pages = {575–579}, numpages = {5}, keywords = {Representation theory, Symmetric group, Alternating group, Cayley graphs, Derangements, Erdos–Ko–Rado combinatorics} } @MISC {WildonBlog, TITLE = {The sum of all hook characters}, AUTHOR = {Mark Wildon}, HOWPUBLISHED = {Wildon's Weblog}, URL = {https://wildonblog.wordpress.com/2019/04/02/character-values-on-the-sum-of-hook-partitions/} } @MISC {WildonBlog2, TITLE = {Sylow subgroups of symmetric groups}, AUTHOR = {Mark Wildon}, HOWPUBLISHED = {Wildon's Weblog}, URL = {https://wildonblog.wordpress.com/2016/11/27/sylow-subgroups-of-symmetric-groups/} } @MISC {YuanMO, TITLE = {Permutations with all cycles odd length and permutations with all cycles even length}, AUTHOR = {Qiaochu Yuan}, HOWPUBLISHED = {MathOverflow}, NOTE = {(version: 2015-05-19)}, URL = {https://mathoverflow.net/q/207062} } @article{Humphreys87, author = {J. E. Humphreys}, title = {{The Steinberg representation}}, volume = {16}, journal = {Bulletin (New Series) of the American Mathematical Society}, number = {2}, publisher = {American Mathematical Society}, pages = {247 -- 263}, year = {1987}, } @misc{Ebrahimi24, title={Cayley graphs on $p$-solvable groups generated by $p$-singular elements}, author={Mahdi Ebrahimi}, year={2024}, eprint={2406.10497}, archivePrefix={arXiv}, primaryClass={math.CO}, url={https://arxiv.org/abs/2406.10497}, } @book{Diaconis88, added-at = {2010-02-04T21:40:41.000+0100}, address = {Hayward, CA}, author = {Diaconis, Persi}, biburl = {http://www.bibsonomy.org/bibtex/2933838b3e918380eb835383259944baf/peter.ralph}, description = {MR: Publications results for "MR Number=(964069)"}, interhash = {f8e3d552ac7a2a48d97ec0820620e592}, intrahash = {933838b3e918380eb835383259944baf}, isbn = {0-940600-14-5}, keywords = {discrete_fourier_transform reference representation_theory}, mrclass = {60-02 (20C99 62-02)}, mrnumber = {MR964069 (90a:60001)}, mrreviewer = {Philippe Bougerol}, pages = {vi+198}, publisher = {Institute of Mathematical Statistics}, series = {Institute of Mathematical Statistics Lecture Notes---Monograph Series, 11}, timestamp = {2010-02-04T21:40:41.000+0100}, title = {Group {R}epresentations in {P}robability and {S}tatistics}, url = {http://projecteuclid.org/euclid.lnms/1215467407}, year = 1988 }