Alternating sign matrices with one 1 under vertical reflection
Abstract
We define a bijection that transforms an alternating sign matrix A with one 1 into a pair (N,E) where N is a (so called) ``neutral'' alternating sign matrix (with one 1) and E is an integer. The bijection preserves the classical parameters of Mills, Robbins and Rumsey as well as three new parameters (including E). It translates vertical reflection of A into vertical reflection of N. A hidden symmetry allows the interchange of E with one of the remaining two new parameters. A second bijection transforms (N,E) into a configuration of lattice paths called ``mixed configuration''.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 January 2004
 arXiv:
 arXiv:math/0401339
 Bibcode:
 2004math......1339L
 Keywords:

 Combinatorics
 EPrint:
 15 pages with 9 figures