Half-turn symmetric FPLs with rare couplings and tilings of hexagons

DOI10.1016/J.TCS.2012.02.043zbMath1301.05061arXiv1109.0366OpenAlexW2094097540MaRDI QIDQ391412

Jean-Christophe Aval, Philippe Duchon

Publication date: 10 January 2014

Published in: Theoretical Computer Science (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1109.0366

zbMATH Keywords

fully packed loop configurationstilings of the hexagon

Mathematics Subject Classification ID

Other designs, configurations (05B30) Combinatorial aspects of tessellation and tiling problems (05B45)

Uses Software

• ROBBINS

Cites Work

• Proof of the Razumov-Stroganov conjecture
• \(O(1)\) loop model with different boundary conditions and symmetry classes of alternating-sign matrices
• Binomial determinants, paths, and hook length formulae
• Advanced determinant calculus
• A large dihedral symmetry of the set of alternating sign matrices
• On the number of fully packed loop configurations with a fixed associated matching
• Symmetry classes of alternating-sign matrices under one roof
• Proof of the alternating sign matrix conjecture
• Four symmetry classes of plane partitions under one roof
• Loops, matchings and alternating-sign matrices
• Combinatorial nature of the ground-state vector of the \(\mathrm{O}(1)\) loop model
• On the link pattern distribution of quarter-turn symmetric FPL configurations
• Enumeration of perfect matchings in graphs with reflective symmetry

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