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

dmtcs:3644 - Discrete Mathematics & Theoretical Computer Science, January 1, 2008, DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008) - https://doi.org/10.46298/dmtcs.3644
On the link pattern distribution of quarter-turn symmetric FPL configurationsArticle

Authors: Philippe Duchon 1

  • 1 Laboratoire Bordelais de Recherche en Informatique

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.

https://doi.org/10.46298/dmtcs.3644
Source: HAL:hal-01185180v1
Volume: DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008)
Section: Proceedings
Published on: January 1, 2008
Imported on: May 10, 2017
Keywords: fully packed loop model,rhombus tilings,plane partitions,nonintersecting lattice paths,[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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