Eulerian numbers associated with arithmetical progressions
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.
scientific article; zbMATH DE number 6873092
scientific article