Proof of two conjectures of Zuber on fully packed loop configurations

DOI10.1016/j.jcta.2004.06.006zbMath1054.05005arXivmath/0312217OpenAlexW2950960254WikidataQ123253518 ScholiaQ123253518MaRDI QIDQ1881686

Fabrizio Caselli, Christian Krattenthaler

Publication date: 14 October 2004

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0312217

zbMATH Keywords

Young tableauxrhombus tilingsplane partitionsnon-intersecting lattice pathsfully packed loop modelhook-content formula

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Combinatorial aspects of representation theory (05E10) Exactly solvable models; Bethe ansatz (82B23) Combinatorial aspects of tessellation and tiling problems (05B45)

Related Items (5)

Fully packed loop configurations in a triangle ⋮ On some ground state components of the O(1) loop model ⋮ Proof of the Razumov-Stroganov conjecture ⋮ On some polynomials enumerating fully packed loop configurations ⋮ Determinant formulae for some tiling problems and application to fully packed loops.

Cites Work

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• Combinatorial nature of the ground-state vector of the \(\mathrm{O}(1)\) loop model
• Exact expressions for correlations in the ground state of the dense O(1) loop model
• The Problem of the Calissons
• Critical behaviour of the fully packed loop model on the square lattice
• Theory and Application of Plane Partitions. Part 2
• Enumeration of Lozenge tilings of hexagons with a central triangular hole
• Lattice path proofs for determinantal formulas for symplectic and orthogonal characters

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