A simple proof on the number of $(3 \times n)$-Latin rectangles based on a set of $λ$ elements
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910521311100928 |
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| author | Thengarnanchai, Pantaree Kaemawichanurat, Pawaton Ruksasakchai, Watcharintorn Klamsakul, Natawat |
| author_facet | Thengarnanchai, Pantaree Kaemawichanurat, Pawaton Ruksasakchai, Watcharintorn Klamsakul, Natawat |
| contents | In 1980, Athreya, Pranesachar and Singhi established the chromatic polynomial of $(3 \times n)$-Latin rectangles whose entries based on a set $\{1, 2, ..., λ\}$ in which $λ\geq n$. Their proof requires Möbius inversion formula and lattice partitions. In this paper, we present a simpler proof by using the idea of mathematical induction and appropriate coloring. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_07378 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A simple proof on the number of $(3 \times n)$-Latin rectangles based on a set of $λ$ elements Thengarnanchai, Pantaree Kaemawichanurat, Pawaton Ruksasakchai, Watcharintorn Klamsakul, Natawat Combinatorics In 1980, Athreya, Pranesachar and Singhi established the chromatic polynomial of $(3 \times n)$-Latin rectangles whose entries based on a set $\{1, 2, ..., λ\}$ in which $λ\geq n$. Their proof requires Möbius inversion formula and lattice partitions. In this paper, we present a simpler proof by using the idea of mathematical induction and appropriate coloring. |
| title | A simple proof on the number of $(3 \times n)$-Latin rectangles based on a set of $λ$ elements |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2407.07378 |