Georgia Institute of Technology College of Sciences

In his works Carlitz defined and investigated a few generalizations of the Eulerian numbers and polynomials. For most of those generalizations he provided also a combinatorial interpretation. The classical Eulerian numbers and some of their generalizations are connected to combinatorial statistics on permutations. Carlitz intended to provide a combinatorial interpretation also to his degenerate Eulerian numbers. However since their introduction in 1979 these numbers had a pure analytic character. In this talk we consider a combinatorial model that generalizes the standard definition of permutations and show its relation to the degenerate Eulerian numbers.