On the link pattern distribution of quarter-turn symmetric FPL configurations

2007/11/19 by Philippe Duchon, Duchon, Philippe
Engineering · Mathematics · #05A15 (primary) 05B45 #82B20 (secondary) #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Geometric and Algebraic Topology #graph theory and CDMA systems #math.CO #msc:05A15 #msc:05B45 #msc:82B20

paper · pdf · doi:10.48550/arxiv.0711.2871

12 pages, 6 figures. Submitted to FPSAC 2008

arxiv created 2007/11/19 · openalex publication_date 2007/11/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present new conjectures on the distribution of link patterns for fully-packed loop (FPL) configurations that are invariant, or almost invariant, under a quarter turn rotation, extending previous conjectures of Razumov and Stroganov and of de Gier. We prove a special case, showing that the link pattern that is conjectured to be the rarest does have the prescribed probability. As a byproduct, we get a formula for the enumeration of a new class of quasi-symmetry of plane partitions.

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