The degenerate Eulerian numbers and combinatorics behind them

Combinatorics Seminar
Friday, October 8, 2021 - 3:00pm for 1 hour (actually 50 minutes)
Skiles 005
Orli Herscovici – Georgia Institute of Technology – orli.herscovici@gmail.com
Anton Bernshteyn

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.