Ilse Fischer
u:find@Universität Wien
Papers:
- (with Florian Schreier-Aigner) "(-1)-Enumerations of arrowed Gelfand-Tsetlin patterns’’, 2023, companion.nb and data.mx
- "Bounded Littlewood identity related to alternating sign matrices’’,
arXiv:2301.00175
- (with Hans Höngesberg) "Alternating sign matrices with reflective symmetry and plane partitions: n+3 pairs of equivalent statistics",
arXiv:2207.04469
- (with Florian Schreier-Aigner) "Alternating sign matrices and totally symmetric plane partitions,
arXiv:2201.13142
- (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.
- "Computations versus bijections in tiling counting’’,
Adv. Appl. Math. 142 (2023), 49pp.
- (with Matjaž Konvalinka) "The mysterious story of square ice, piles of cubes, and bijections",
PNAS 2020, PDF
- (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
- (with Matjaž Konvalinka) "The first bijective proof of the refined ASM theorem",
Sem. Lothar. Combin. 84B, Proceedings of FPSAC'20. PDF
- (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
- (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
- (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
- (with Manjil P. Saikia ) "Refined Enumeration of Symmetry Classes of Alternating Sign Matrices",
J. Combin. Theory Ser. A 178 (2021).
arXiv:1906.07723
- (with Arvind Ayyer ) "Bijective proofs of skew Schur polynomial factorizations",
J. Combin. Theory Ser. A 174 (2020).
arXiv:1905.05226
- A constant tern approach to enumerating alternating sign trapezoids",
Adv. Math. 356 (2019).
arXiv:1804.08681
- "Enumeration of alternating sign triangles using a constant term approach",
Trans. Amer. Math. Soc. 372 (2019), 1485--1508.
arXiv:1804.03630
- "Constant term formulas for refined enumerations of Gog and Magog trapezoids",
J. Combin. Theory Ser. A 158 (2018), 560--604.
arXiv:1804.07054
- (with Arvind Ayyer and Roger Behrend ) "Extreme diagonally and antidiagonally symmetric alternating sign matrices of odd order",
Adv. Math. 367 (2020).
arXiv:1611.03823
- "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
- "Counting integer points in polytopes associated with directed graphs",
Adv. Appl. Math. 79 (2016), 125-153. PDF
- (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
- (with Mihai Ciucu) "Lozenge tilings of hexagons with arbitrary dents ",
Adv. Appl. Math. 73 (2016), 1-22.
arXiv:1412.3945
- (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
- (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.
- (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
- (with Martina Juhnke-Kubitzke ) "Spectra and eigenvectors of the Segre transformation",
Adv. Appl. Math. 56 (2014), 1-19.
arXiv:1303:5358
- (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
- (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
- (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
- "Sequences of labeled trees related to Gelfand-Tsetlin patterns ",
Adv. Appl. Math. 49 (2012), 165 -- 195.
arXiv:1104.0568v1
- "Linear relations of refined enumerations of alternating sign matrices ",
J. Combin. Theory Ser. A 119 (2012), no. 2, 556 -- 578.
arXiv:1008.0527v1
- "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
- (with Dan Romik) "More refined enumerations of alternating sign matrices",
Adv. Math 222 (2009), Issue 6, 2004 -- 2035.
arXiv:0903.5073
Mathematica-Package
- "The operator formula for monotone triangles -- simplified proof and three generalizations",
J. Combin. Theory Ser. A. 117 (2010), 1143 -- 1157.
arXiv:0903.4628
- "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
- "A new proof of the refined alternating sign matrix theorem",
J. Combin. Theory Ser. A 114 (2007), no. 2, 253 -- 264.
math.CO/0507270
- "The number of monotone triangles with prescribed bottom row",
Adv. Appl. Math. 37 (2006), no. 2, 249 -- 267.
math.CO/0501102
- (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.
- "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
- "A method for proving polynomial enumeration formulas",
J. Combin. Theory Ser. A 111 (2005), 37 -- 58.
math.CO/0301103
- (with Charles H. C. Little) "Even circuits of prescribed clockwise parity",
Elect. J. Combin. 10, R45, 20 pages.
math.CO/0203281
- "A symmetry theorem on a modified jeu de taquin",
European J. Combin. 23 (2002), 929 -- 936.
math.CO/0112263
- "A bijective proof of the hook length formula for shifted standard tableaux", preprint, December 2001.
math.CO/0112261
- "Moments of inertia associated with the lozenge tilings of a hexagon",
Sem. Lothar. Combin. 45 (2000/01), Art B45f, 14pp. (electronic).
math.CO/0012126
- (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
- (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
- "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!
Theses:
My very first paper: