Philippe Nadeau - Fully Packed Loop configurations in a triangle and Littlewood Richardson coefficients

dmtcs:2881 - Discrete Mathematics & Theoretical Computer Science, January 1, 2010, DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010) - https://doi.org/10.46298/dmtcs.2881
Fully Packed Loop configurations in a triangle and Littlewood Richardson coefficientsArticle

Authors: Philippe Nadeau ORCID1,2

We are interested in Fully Packed Loops in a triangle (TFPLs), as introduced by Caselli at al. and studied by Thapper. We show that for Fully Packed Loops with a fixed link pattern (refined FPL), there exist linear recurrence relations with coefficients computed from TFPL configurations. We then give constraints and enumeration results for certain classes of TFPL configurations. For special boundary conditions, we show that TFPLs are counted by the famous Littlewood Richardson coefficients.


Volume: DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010)
Section: Proceedings
Published on: January 1, 2010
Imported on: January 31, 2017
Keywords: Razumov Stroganov conjecture,Fully Packed Loop,Littlewood―Richardson coefficients,[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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