The number of monotone triangles with prescribed bottom row

Abstract

We show that the number of monotone triangles with prescribed bottom row (k_1,...,k_n) is given by a simple product formula which remarkably involves (shift) operators. Monotone triangles with bottom row (1,2,...,n) are in bijection with $n\times n$ alternating sign matrices.

References in corpus (2)

• Another proof of the alternating sign matrix conjecture
• Proof of the Refined Alternating Sign Matrix Conjecture