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arXiv · 2407.07378

A simple proof on the number of $(3 \times n)$-Latin rectangles based on a set of $λ$ elements

Pantaree Thengarnanchai·Pawaton Kaemawichanurat·Watcharintorn Ruksasakchai·Natawat Klamsakul
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Abstract

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.

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Pantaree Thengarnanchai, Pawaton Kaemawichanurat, Watcharintorn Ruksasakchai, Natawat Klamsakul. 2024-07-10. A simple proof on the number of $(3 \times n)$-Latin rectangles based on a set of $λ$ elements. https://arxiv.org/abs/2407.07378

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