The number of rhombus tilings of a symmetric hexagon which contain a fixed rhombus on the symmetry axis. II

DOI10.1006/eujc.1999.0367zbMath0965.05010arXivmath/9909038OpenAlexW2101527974MaRDI QIDQ1580673

Christian Krattenthaler, Markus Fulmek

Publication date: 2 August 2001

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

Full work available at URL: https://arxiv.org/abs/math/9909038

zbMATH Keywords

symmetryHankel determinantBernoulli numbershexagonrhombus tilingshypergeometric transformation

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Combinatorial aspects of partitions of integers (05A17) Generalized hypergeometric series, ({}_pF_q) (33C20) Combinatorial aspects of tessellation and tiling problems (05B45) Tilings in (2) dimensions (aspects of discrete geometry) (52C20)

Related Items

A \(q\)-enumeration of lozenge tilings of a hexagon with four adjacent triangles removed from the boundary, Hankel determinants of sequences related to Bernoulli and Euler polynomials, \(q\)-Bernoulli-Carlitz numbers and continued fractions, Hankel determinants, Hahn polynomials, and a formula of Krattenthaler, Moments of orthogonal polynomials and exponential generating functions, A non-automatic (!) application of Gosper's algorithm evaluates a determinant from tiling enumeration, Orthogonal polynomials and Hankel determinants for certain Bernoulli and Euler polynomials, Gaussian Hypergeometric series and supercongruences, Enumeration of rhombus tilings of a hexagon which contain a fixed rhombus in the centre, The number of rhombus tilings of a symmetric hexagon which contain a fixed rhombus on the symmetry axis. I, The five-vertex model and boxed plane partitions, Fourier transform on high-dimensional unitary groups with applications to random tilings, Lozenge tilings of a hexagon with a horizontal intrusion

Uses Software

• gfun
• GeneratingFunctions

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