Binomial determinants for tiling problems yield to the holonomic ansatz

DOI10.1016/j.ejc.2021.103437zbMath1480.15005arXiv2105.08539OpenAlexW3161239011MaRDI QIDQ2237864

Hao Du, Christoph Koutschan, Elaine Wong, Thotsaporn ``Aek Thanatipanonda

Publication date: 28 October 2021

Published in: European Journal of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2105.08539

zbMATH Keywords

determinantbinomial coefficientrhombus tilingholonomic ansatz

Mathematics Subject Classification ID

Factorials, binomial coefficients, combinatorial functions (05A10) Combinatorial aspects of matrices (incidence, Hadamard, etc.) (05B20) Determinants, permanents, traces, other special matrix functions (15A15) Combinatorial aspects of tessellation and tiling problems (05B45) Tilings in (2) dimensions (aspects of discrete geometry) (52C20)

Related Items (1)

A Unified Approach to Unimodality of Gaussian Polynomials

Uses Software

• DLMF
• HolonomicFunctions
• DODGSON
• DET

Cites Work

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• Advanced computer algebra for determinants
• The concrete tetrahedron. Symbolic sums, recurrence equations, generating functions, asymptotic estimates
• Descending plane partitions and rhombus tilings of a hexagon with a triangular hole
• Selberg integrals, Askey-Wilson polynomials and lozenge tilings of a hexagon with a triangular hole
• Binomial determinants, paths, and hook length formulae
• Plane partitions. III: The weak Macdonald conjecture
• A holonomic systems approach to special functions identities
• The method of creative telescoping
• Advanced determinant calculus
• Theory of non-commutative polynomials
• Enumeration of Lozenge tilings of hexagons with cut-off corners
• A curious family of binomial determinants that count rhombus tilings of a holey hexagon
• Creative telescoping on multiple sums
• Proof of two conjectures of Ciucu and Krattenthaler on the enumeration of lozenge tilings of hexagons with cut off corners
• The holonomic ansatz. II: Automatic discovery(!) and proof(!!) of holonomic determinant evaluations
• A Schur function identity related to the \((-1)\)-enumeration of self-complementary plane partitions
• Advanced determinant calculus: a complement
• Advanced applications of the holonomic systems approach
• Creative Telescoping for Holonomic Functions
• On the Vector Representations of Induced Matroids
• Enumeration of Lozenge tilings of hexagons with a central triangular hole
• Determinants through the looking glass

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