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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 January 2005
 DOI:
 10.48550/arXiv.math/0501102
 arXiv:
 arXiv:math/0501102
 Bibcode:
 2005math......1102F
 Keywords:

 Combinatorics