New Eulerian numbers of type \(D\) (Q252858)
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scientific article; zbMATH DE number 6549747
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | New Eulerian numbers of type \(D\) |
scientific article; zbMATH DE number 6549747 |
Statements
New Eulerian numbers of type \(D\) (English)
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4 March 2016
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Summary: We introduce a new array of type \(D\) Eulerian numbers, different from that studied by \textit{F. Brenti} [Eur. J. Comb. 15, No. 5, 417--441 (1994; Zbl 0809.05012)], \textit{C.-O. Chow} [ibid. 24, No. 4, 391--408 (2003; Zbl 1033.05003)] and \textit{M. Hyatt} [``Recurrences for Eulerian polynomials of type B and type D'', Preprint, \url{arXiv:1404.3110}]. We find in particular the recurrence relation, Worpitzky formula and the generating function. We also find the probability distributions whose moments are Eulerian polynomials of type \(A\), \(B\) and \(D\).
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Eulerian numbers
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signed permutations
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moments of a probability measure
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