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Article Dans Une Revue Advances in Applied Mathematics Année : 2011

On some polynomials enumerating Fully Packed Loop configurations

Résumé

We are interested in the enumeration of Fully Packed Loop configurations on a grid with a given noncrossing matching. By the recently proved Razumov--Stroganov conjecture, these quantities also appear as groundstate components in the Completely Packed Loop model. When considering matchings with p nested arches, these numbers are known to be polynomials in p. In this article, we present several conjectures about these polynomials: in particular, we describe all real roots, certain values of these polynomials, and conjecture that the coefficients are positive. The conjectures, which are of a combinatorial nature, are supported by strong numerical evidence and the proofs of several special cases. We also give a version of the conjectures when an extra parameter tau is added to the equations defining the groundstate of the Completely Packed Loop model.

Dates et versions

hal-00863299 , version 1 (18-09-2013)

Identifiants

Citer

Tiago Fonseca, Philippe Nadeau. On some polynomials enumerating Fully Packed Loop configurations. Advances in Applied Mathematics, 2011, 47 (3), pp.434-462. ⟨10.1016/j.aam.2010.11.003⟩. ⟨hal-00863299⟩
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