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The characterization of an Alternating Sign Matrix using a triplet
- Publication Year :
- 2024
-
Abstract
- Alternating Sign Matrix(ASM for short) is a square matrix which is consist 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 $({a}_{i, j}, {c}_{i, j}, {r}_{i, j})$ for each entry of an ASM. We also define a \textsl{track} for each index of height function, and state more properties of height function.<br />Comment: 29 pages, 25 figures
- Subjects :
- Mathematics - Combinatorics
05A19(Primary), 05A05, 05A10(Secondary)
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2403.01275
- Document Type :
- Working Paper