A combinatorial approach to the power of 2 in the number of involutions

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Kim, Dongsu
Kim, Jang Soo
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Abstract
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We provide a combinatorial approach to the largest power of $p$ in the number of permutations $\pi$ with $\pi^p=1$, for a fixed prime number $p$. With this approach, we find the largest power of $2$ in the number of involutions, in the signed sum of involutions and in the numbers of even or odd involutions.
Comment: 13 pages
Keywords
Mathematics - Combinatorics, Mathematics - Number Theory, 05A05, 11B75
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