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

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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Philippe Duchon. On the link pattern distribution of quarter-turn symmetric FPL configurations. 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008), 2008, Viña del Mar, Chile. pp.331-342, ⟨10.46298/dmtcs.3644⟩. ⟨hal-01185180⟩



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