A note on the total number of cycles of even and odd permutations |
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| Authors: | Jang Soo Kim |
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| Affiliation: | LIAFA, Université Paris Diderot, 175 rue du Chevaleret, 75013 Paris, France |
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| Abstract: | ![]()
We prove bijectively that the total number of cycles of all even permutations of [n]={1,2,…,n} and the total number of cycles of all odd permutations of [n] differ by (−1)n(n−2)!, which was stated as an open problem by Miklós Bóna. We also prove bijectively the following more general identity: |
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| Keywords: | Cycles of permutations Sign-reversing involution |
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