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arXiv · 1811.09606

The Problem of Pawns

Tricia Muldoon Brown
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Abstract

Using a bijective proof, we show the number of ways to arrange a maximum number of nonattacking pawns on a $2m\times 2m$ chessboard is ${2m\choose m}^2$, and more generally, the number of ways to arrange a maximum number of nonattacking pawns on a $2n \times 2m$ chessboard is ${m+n\choose n}^2$.

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Tricia Muldoon Brown. 2018-11-24. The Problem of Pawns. https://arxiv.org/abs/1811.09606

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