Mathematical Journal of Okayama University 67巻 1号
2025-01 発行
The characterizations of an alternating sign matrices using a triplet
Ohmoto, Toyokazu
Department of Mathematics, Faculty of Science, Okayama University
Publication Date
2025-01
Abstract
An alternating sign matrix (ASM for short) is a square matrix which consists of 0, 1 and −1. In this paper, we characterize an ASM by showing a bijection between alternating sign matrix and six vertex model, and a bijection between six vertex model and height function.
In order to show these bijections, we define a triplet (ai,j , ci,j , ri,j) for each entry of an ASM. We also define a track for each index of height function, and state more properties of height function.
Keywords
Alternating sign matrix
six vertex model
height function
Comments
Mathematics Subject Classification. Primary 05A19; Secondary 05A05, 05E10.
ISSN
0030-1566
NCID
AA00723502
