Probabilistic degenerate derangement polynomials
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929538636709888 |
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| author | Kim, Taekyun Kim, Dae San |
| author_facet | Kim, Taekyun Kim, Dae San |
| contents | In combinatorics, a derangement is a permutation of the elements of a set, such that no element appears in its original position. The number of derangement of an n-element set is called the nth derangement number. Recently, the degenerate derangement numbers and polynomials have been studied as degenerate versions. Let Y be a random variable whose moment generating function exists in a neighborhood of the origin. In this paper, we study probabilistic extension of the degenerate derangement numbers and polynomials, namely the probabilistic degenerate derangement numbers and polynomials associated with Y. In addition, we consider the probabilistic degenerate r-derangement numbers associated with Y and the probabilistic degenerate derangement polynomila of the second kind associated with Y. We derive some properties, explicit expressions, certain identities and recurrence relations for those polynomials and numbers. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_09394 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Probabilistic degenerate derangement polynomials Kim, Taekyun Kim, Dae San Number Theory 11B73, 11B83 In combinatorics, a derangement is a permutation of the elements of a set, such that no element appears in its original position. The number of derangement of an n-element set is called the nth derangement number. Recently, the degenerate derangement numbers and polynomials have been studied as degenerate versions. Let Y be a random variable whose moment generating function exists in a neighborhood of the origin. In this paper, we study probabilistic extension of the degenerate derangement numbers and polynomials, namely the probabilistic degenerate derangement numbers and polynomials associated with Y. In addition, we consider the probabilistic degenerate r-derangement numbers associated with Y and the probabilistic degenerate derangement polynomila of the second kind associated with Y. We derive some properties, explicit expressions, certain identities and recurrence relations for those polynomials and numbers. |
| title | Probabilistic degenerate derangement polynomials |
| topic | Number Theory 11B73, 11B83 |
| url | https://arxiv.org/abs/2410.09394 |