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Fully Packed Loop configurations in a triangle and Littlewood Richardson coefficients

Abstract : 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.
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Philippe Nadeau. Fully Packed Loop configurations in a triangle and Littlewood Richardson coefficients. 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010), 2010, San Francisco, United States. pp.425-436. ⟨hal-01186310⟩

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