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

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.