Séminaire Lotharingien de Combinatoire, 78B.60 (2017), 12 pp.
Refined Enumerations of Alternating Sign Triangles
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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