Ilse Fischer

u:find@Universität Wien  

Combinatorics Group@Universität Wien

Papers:

1.       (with Florian Schreier-Aigner) "(-1)-Enumerations of arrowed Gelfand-Tsetlin patterns’’, 2023, companion.nb and data.mx 
2.   "Bounded Littlewood identity related to alternating sign matrices’’, 
   arXiv:2301.00175
3.       (with Hans Höngesberg) "Alternating sign matrices with reflective symmetry and plane partitions: n+3 pairs of equivalent statistics",  
   arXiv:2207.04469
4.       (with Florian Schreier-Aigner) "Alternating sign matrices and totally symmetric plane partitions,  
   arXiv:2201.13142
5.       (with Florian Schreier-Aigner) "The relation between alternating sign matrices and descending plane partitions: n+3 pairs of equivalent statistics",  
   arXiv:2106.11568, to appear in Adv. Math.
6.       "Computations versus bijections in tiling counting’’,
   Adv. Appl. Math. 142 (2023), 49pp.
7.       (with Matjaž Konvalinka) "The mysterious story of square ice, piles of cubes, and bijections",
   PNAS 2020, PDF 
8.       (with Florian Schreier-Aigner, Matjaž Konvalinka, Philippe Nadeau, and Vasu Tewari) "Alternating Sign Matrices and Totally Symmetric Plane Partitions",
   Sem. Lothar. Combin. 84B, Proceedings of FPSAC'20.
   arXiv:2005.12448 
9.       (with Matjaž Konvalinka) "The first bijective proof of the refined ASM theorem",
   Sem. Lothar. Combin. 84B, Proceedings of FPSAC'20. PDF 
10.         (with Matjaž Konvalinka) "A bijective proof of the ASM theorem, Part II: ASM enumeration and ASM-DPP relation",
    Int. Math. Res. Not. IMRN 2022, no. 10, 7203-7230.
    arXiv:1912.01354 
11. (with Mihai Ciucu) "Lozenge tilings of hexagons with removed core and satellites",
    arXiv:1910.11004, to appear in Annales de l’Institut Henri Poincaré D
12. (with Matjaž Konvalinka ) "A bijective proof of the ASM theorem, Part I: the operator formula",
    Elect. J. Combin. 27, P3.35, 29 pages.
    arXiv:1910.04198 
13. (with Manjil P. Saikia ) "Refined Enumeration of Symmetry Classes of Alternating Sign Matrices",
    J. Combin. Theory Ser. A 178 (2021).
    arXiv:1906.07723
14. (with Arvind Ayyer ) "Bijective proofs of skew Schur polynomial factorizations",
    J. Combin. Theory Ser. A 174 (2020).
    arXiv:1905.05226 
15. A constant tern approach to enumerating alternating sign trapezoids",
    Adv. Math. 356 (2019).
    arXiv:1804.08681 
16. "Enumeration of alternating sign triangles using a constant term approach",
    Trans. Amer. Math. Soc. 372 (2019), 1485--1508.
    arXiv:1804.03630 
17. "Constant term formulas for refined enumerations of Gog and Magog trapezoids",
    J. Combin. Theory Ser. A 158 (2018), 560--604.
    arXiv:1804.07054 
18. (with Arvind Ayyer and Roger Behrend ) "Extreme diagonally and antidiagonally symmetric alternating sign matrices of odd order",
    Adv. Math. 367 (2020).
    arXiv:1611.03823 
19. "Short proof of the ASM theorem avoiding the six-vertex model",
    J. Combin. Theory Ser. A 144 (2016), 139-156. Fifty Years of the Journal of Combinatorial Theory! PDF
20. "Counting integer points in polytopes associated with directed graphs",
    Adv. Appl. Math. 79 (2016), 125-153. PDF 
21. (with Roger Behrend and Matjaž Konvalinka ) "Diagonally and antidiagonally symmetric alternating sign matrices of odd order",
    Adv. Math. 315 (2017), 324--365.
    arXiv:1512.06030 
22. (with Mihai Ciucu) "Lozenge tilings of hexagons with arbitrary dents ",
    Adv. Appl. Math. 73 (2016), 1-22.
    arXiv:1412.3945 
23. (with Sabine Beil and Philippe Nadeau ) "Wieland gyration for triangular fully packed loop configurations ",
    Elect. J. Combin. 22, P1.26, 17 pages.
    arXiv:1406.1657 
24. (with Lukas Riegler ) "Vertically symmetric alternating sign matrices and a multivariate Laurent polynomial identity",
    Elect. J. Combin. 22, P1.5, 32 pages.
    arXiv:1403.0535
    An Oberwolfachreport on this topic.
25. (with Mihai Ciucu ) "Proof of two conjectures of Ciucu and Krattenthaler on the enumeration of lozenge tilings of hexagons with cut off corners",
    J. Combin. Theory Ser. A 133 (2015), 228-250.
    arXiv:1309.4640 
26. (with Martina Juhnke-Kubitzke ) "Spectra and eigenvectors of the Segre transformation",
    Adv. Appl. Math. 56 (2014), 1-19.
    arXiv:1303:5358 
27. (with Philippe Nadeau ) "Fully Packed Loops in a triangle: matchings, paths and puzzles",
    J. Combin. Theory Ser. A 130 (2015), 64-118.
    arXiv:1209.1262 
28. (with Mihai Ciucu )
    "A triangular gap of size two in a sea of dimers on a 60 degree angle", J. Phys. A: Math. Theor. 45 (2012).
    PDF 
29. (with Lukas Riegler ) "Combinatorial Reciprocity for Monotone Triangles",
    J. Combin. Theory Ser. A 120 (2013), 1372 - 1393.
    arXiv:1111.2695
    accepted for a FPSAC12 talk 
30. "Sequences of labeled trees related to Gelfand-Tsetlin patterns ",
    Adv. Appl. Math. 49 (2012), 165 -- 195.
    arXiv:1104.0568v1 
31. "Linear relations of refined enumerations of alternating sign matrices ",
    J. Combin. Theory Ser. A 119 (2012), no. 2, 556 -- 578.
    arXiv:1008.0527v1 
32. "Refined enumerations of alternating sign matrices: monotone (d,m)-trapezoids with prescribed top and bottom row",
    J. Alg. Combin. 33 (2011), no. 2, 239 -- 257.
    arXiv:0907.0401 
33. (with Dan Romik) "More refined enumerations of alternating sign matrices",
    Adv. Math 222 (2009), Issue 6, 2004 -- 2035.
    arXiv:0903.5073
    Mathematica-Package
34. "The operator formula for monotone triangles -- simplified proof and three generalizations",
    J. Combin. Theory Ser. A. 117 (2010), 1143 -- 1157.
    arXiv:0903.4628 
35. "An operator formula for the number of halved monotone triangles with prescribed bottom row",
    J. Combin. Theory Ser. A 116 (2009), no. 3, 515 -- 538.
    math.CO/0702637
36. "A new proof of the refined alternating sign matrix theorem",
    J. Combin. Theory Ser. A 114 (2007), no. 2, 253 -- 264.
    math.CO/0507270 
37. "The number of monotone triangles with prescribed bottom row",
    Adv. Appl. Math. 37 (2006), no. 2, 249 -- 267.
    math.CO/0501102 
38. (with Gerald Gruber, Franz Rendl and Renata Sotirov) "Computational experience with a bundle approach for semidefinite cutting plane relaxations of Max-Cut and Equipartition",
    Math. Program., Ser. B 105 (2006), 451 -- 469. 
39. "Another refinement of the Bender-Knuth (ex-)Conjecture",
    European J. Combin. 27 (2006), 290 -- 321.
    math.CO/0401235
    Mathematica-file with some hypergeometric identities used in the paper
40. "A method for proving polynomial enumeration formulas",
    J. Combin. Theory Ser. A 111 (2005), 37 -- 58.
    math.CO/0301103
41. (with Charles H. C. Little) "Even circuits of prescribed clockwise parity",
    Elect. J. Combin. 10, R45, 20 pages.
    math.CO/0203281
42. "A symmetry theorem on a modified jeu de taquin",
    European J. Combin. 23 (2002), 929 -- 936.
    math.CO/0112263
43. "A bijective proof of the hook length formula for shifted standard tableaux", preprint, December 2001.
    math.CO/0112261
44. "Moments of inertia associated with the lozenge tilings of a hexagon",
    Sem. Lothar. Combin. 45 (2000/01), Art B45f, 14pp. (electronic).
    math.CO/0012126
45. (with Charles H.C. Little) "A characterisation of Pfaffian near bipartite graphs",
    J. Combin. Theory Ser. B 82 (2001), no. 2, 175 -- 222.
    math.CO/0002062
46. (with Charles H. C. Little and Franz Rendl) "Towards a characterisation of Pfaffian near bipartite graphs",
    Discrete Math. 244 (2002), 279 -- 297.
    math.CO/9909026
47. "Enumeration of rhombus tilings of a hexagon which contain a fixed rhombus in the centre",
    J. Combin. Theory Ser. A 96 (2001), no. 1, 31 -- 88.
    math.CO/9906102 

Some talks:

• Alternating Sign Arrays and Plane Partitions, SLC 90   
• New Littlewood-type identities and the sequence 1, 4, 60, 3328,…      
• Bounded Littlewood-type identities and alternating sign matrices 
• Alternating sign matrices and descending plane partitions: n+3 pairs of equivalent statistics , Video from ``Lattice Paths, Combinatorics and Interactions, 2021, CIRM 
• Where are the bijections ? Plane partitions and alternating sign matrices
• Bijective proofs of (skew) Schur polynomial factorizations, Video from the 2020 cms winter meeting.
• First bijective proofs of ASM theorems: short and long. Video from FPSAC 2020 and Video from AofA 2020.
• Alternating sign trapezoids and cyclically symmetric lozenge tilings with a central hole
• Extreme DASASMs of odd order
• FPSAC talk on DASASMs
• Proof of the DASASM-conjecture
• Lozenge tilings of hexagons with arbitrary dents, other version
• Extreme DADASMs
• Vertically symmetric alternating sign matrices and a multivariate laurent polynomial identity
• Fully packed loop configurations on a triangle for experts and for newcomers
• An alternative approach to alternating sign matrices
• Sequences of labeled trees related to gelfand-tsetlin patterns
• Refined enumerations of alternating sign matrices
• Die Mathematik des Käse-Kästchen-Spiels (Schüler*innentag)
• A new proof of the refined alternating sign matrix theorem
• The number of monotone triangles with prescribed bottom row
• Die Geschichte der alternierenden Vorzeichenmatrix Vermutung
• Polynomiale Abzählformeln
• A method for proving polynomial enumeration formulas
• A bijective proof of the hook-length formula for shifted standard tableaux
• A youtube talk of my father on education!

• Doctoral Students
• Teaching
• CV
• David P. Robbins Prize 2019 of the AMS: Prize Booklet and Video

Theses:

• "Der Satz von Skolem, Mahler, Lech - ein Ergebnis über die Nullstellen linearer Rekursionsfolgen", Master thesis, Vienna 1997. 
• "Enumeration of perfect matchings: Rhombus tilings and Pfaffian graphs", Doctoral thesis, Vienna 2000. 
• "A polynomial method for the enumeration of plane partitions and alternating sign matrices", Habilitation thesis, Vienna 2005. 

My very first paper:

• "A simple new proof of the Primitive Element Theorem", Vienna 1996.