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Pain, Jean-Christophe
Paris-Saclay University
Computer Science & IT Decision Sciences, Operations Research & Management

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Sum rules for permutations with fixed points involving Stirling numbers of the first kind Pain, Jean-Christophe
Indonesian Journal of Combinatorics Vol 9, No 2 (2025)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2025.9.2.5

Abstract

We propose sum rules for permutations pn(k) of the ensemble {1,2,...,n} with k fixed points, in the form of partial sums of their moments. The corresponding identities involve Stirling numbers of the first kind s(q,r). Using a formula due to Vassilev-Missana and the Schlomlich expression of Stirling numbers, we also deduce sum rules for binomial coefficients. Connections with Bell numbers Bn are outlined.
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