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On some properties of the number of permutations being products of pairwise disjoint $d$-cycles
| Content Provider | Semantic Scholar |
|---|---|
| Author | Miska, Piotr Ulas, Maciej |
| Copyright Year | 2019 |
| Abstract | Let $d\geq 2$ be an integer. In this paper we study arithmetic properties of the sequence $(H_d(n))_{n\in\N}$, where $H_{d}(n)$ is the number of permutations in $S_{n}$ being products of pairwise disjoint cycles of a fixed length $d$. In particular we deal with periodicity modulo a given positive integer, behaviour of the $p$-adic valuations and various divisibility properties. Moreover, we introduce some related families of polynomials and study they properties. Among many results we obtain qualitative description of the $p$-adic valuation of the number $H_{d}(n)$ extending in this way earlier results of Ochiai and Ishihara, Ochiai, Takegehara and Yoshida. |
| File Format | PDF HTM / HTML |
| DOI | 10.1007/s00605-020-01397-5 |
| Alternate Webpage(s) | https://arxiv.org/pdf/1904.03395v1.pdf |
| Alternate Webpage(s) | https://doi.org/10.1007/s00605-020-01397-5 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
