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

DOI10.1007/BF01626027zbMath0917.05004arXivmath/9712244OpenAlexW2569766373MaRDI QIDQ1272360

Markus Fulmek, Christian Krattenthaler

Publication date: 2 August 1999

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

Full work available at URL: https://arxiv.org/abs/math/9712244

zbMATH Keywords

nonintersecting lattice pathsenumeration problemhexagonrhombus tilingsplane partitionslozenge tilingsdeterminant evaluationsmatchings factorization

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 (9)

A \(q\)-enumeration of lozenge tilings of a hexagon with four adjacent triangles removed from the boundary ⋮ Enumeration of lozenge tilings of a hexagon with a shamrock missing on the symmetry axis ⋮ Plethysms of symmetric functions and representations of \(\mathrm{SL}_2(\mathbf{C})\) ⋮ Generalizations of an integral for Legendre polynomials by Persson and Strang ⋮ The five-vertex model and boxed plane partitions ⋮ The number of rhombus tilings of a symmetric hexagon which contain a fixed rhombus on the symmetry axis. II ⋮ Lozenge tilings of a hexagon with a horizontal intrusion ⋮ Advanced determinant calculus: a complement ⋮ Enumeration of Lozenge tilings of hexagons with cut-off corners

Cites Work

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• Proof of a determinant evaluation conjectured by Bombieri, Hunt and van Poorten
• The number of rhombus tilings of a symmetric hexagon which contain a fixed rhombus on the symmetry axis. II
• Nonintersecting paths, pfaffians, and plane partitions
• Generating functions for plane partitions of a given shape
• The Problem of the Calissons
• A new proof of the M-R-R conjecture-including a generalization
• Enumeration of perfect matchings in graphs with reflective symmetry

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