Séminaire Lotharingien de Combinatoire, 78B.60 (2017), 12 pp.

Florian Aigner

Refined Enumerations of Alternating Sign Triangles

Abstract. We generalise alternating sign triangles, which were recently introduced by Ayyer, Behrend and Fischer and shown to be equinumerous with ASMs, to AS-trapezoids and introduce a refinement by Catalan objects. We show that the number of AS-trapezoids associated with a fixed Catalan object is a polynomial in the length of the shorter base of the trapezoid. As a special case we obtain an analogue of a polynomiality theorem for fully packed loops with nested arches.

Received: November 14, 2016. Accepted: February 17, 2017. Final version: April 1, 2017.

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