Eulerian numbers associated with arithmetical progressions (Q1753014)
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scientific article; zbMATH DE number 6873092
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Eulerian numbers associated with arithmetical progressions |
scientific article; zbMATH DE number 6873092 |
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Eulerian numbers associated with arithmetical progressions (English)
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25 May 2018
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Summary: In this paper, we give a combinatorial interpretation of the \(r\)-Whitney-Eulerian numbers by means of coloured signed permutations. This sequence is a generalization of the well-known Eulerian numbers and it is connected to \(r\)-Whitney numbers of the second kind. Using generating functions, we provide some combinatorial identities and the log-concavity property. Finally, we show some basic congruences involving the \(r\)-Whitney-Eulerian numbers.
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Eulerian number
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\(r\)-Whitney number
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\(r\)-Whitney-Eulerian number
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combinatorial identities
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unimodality
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