Fully packed loop configurations : polynomiality and nested arches

Abstract

This extended abstract proves that the number of fully packed loop configurations whose link pattern consists of two noncrossing matchings separated by m nested arches is a polynomial in m. This was conjectured by Zuber (2004) and for large values of m proved by Caselli et al. (2004)

Keywords

• [math.math-co]mathematics [math]/combinatorics [math.co]