Geodesic
Eulerian numbers associated with arithmetical progressions
José L. Ramírez1 ; Sergio N. Villamarin2 ; Diego Villamizar2
1Universidad Nacional de Colombia
2Department of Mathematics, Tulane University
The electronic journal of combinatorics, Tome 25 (2018) no. 1
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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.
DOI : 10.37236/7182
Classification : 11B83, 05A15, 05A19
Mots-clés : Eulerian number, \(r\)-Whitney number, \(r\)-Whitney-Eulerian number, combinatorial identities, unimodality

José L. Ramírez  1   ; Sergio N. Villamarin  2   ; Diego Villamizar  2

1 Universidad Nacional de Colombia
2 Department of Mathematics, Tulane University 
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     title = {Eulerian numbers associated with arithmetical progressions},
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     year = {2018},
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     doi = {10.37236/7182},
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José L. Ramírez; Sergio N. Villamarin; Diego Villamizar. Eulerian numbers associated with arithmetical progressions. The electronic journal of combinatorics, Tome 25 (2018) no. 1. doi: 10.37236/7182

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