An operator formula for the number of halved monotone triangles with prescribed bottom row

Abstract

Monotone triangles are certain triangular arrays of integers, which correspond to $n \times n$ alternating sign matrices when prescribing $(1,2,...,n)$ as bottom row of the monotone triangle. In this article we define halved monotone triangles, a specialization of which correspond to vertically symmetric alternating sign matrices. We derive an operator formula for the number of halved monotone triangles with prescribed bottom row which is analogous to our operator formula for the number of ordinary monotone triangle.