The characterization of an Alternating Sign Matrix using a triplet
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913655080091648 |
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| author | Ohmoto, Toyokazu |
| author_facet | Ohmoto, Toyokazu |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_01275 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The characterization of an Alternating Sign Matrix using a triplet Ohmoto, Toyokazu Combinatorics 05A19(Primary), 05A05, 05A10(Secondary) 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. |
| title | The characterization of an Alternating Sign Matrix using a triplet |
| topic | Combinatorics 05A19(Primary), 05A05, 05A10(Secondary) |
| url | https://arxiv.org/abs/2403.01275 |