Alternating sign matrices with one -1 under vertical reflection
组合数学
2007-05-23 v1
摘要
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''.
引用
@article{arxiv.math/0401339,
title = {Alternating sign matrices with one -1 under vertical reflection},
author = {Pierre Lalonde},
journal= {arXiv preprint arXiv:math/0401339},
year = {2007}
}
备注
15 pages with 9 figures