The signed Eulerian numbers on involutions

M. Barnabei, F. Bonetti, M. Silimbani

Published 2008-03-14Version 1

We define an analogue of signed Eulerian numbers $f_{n,k}$ for involutions of the symmetric group and derive some combinatorial properties of this sequence. In particular, we exhibit both an explicit formula and a recurrence for $f_{n,k}$ arising from the properties of its generating function.