# A new determinant for the Q-enumeration of alternating sign matrices

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Time: 11:00 -- Location: Salle Philippe Flajolet du LIX

We prove a determinantal formula for the $$Q$$-enumeration of alternating sign matrices (ASMs), i.e. a weighted enumeration where each ASM is weighted by $$Q$$ to the power of the number of its $$-1$$'s. Evaluating this determinant leads to closed product formulas and new proofs of the $$1$$-,$$2$$- and $$3$$-enumeration of ASMs. Finally we relate our results to the determinant evaluations of Ciucu, Eisenkölbl, Krattenthaler and Zare (2001), which count weighted cyclically symmetric lozenge tilings of a hexagon with a triangular hole.

Category: seminars
Tags: Combi seminar combinatorics