Recursions for the flag-excedance number in colored permutations groups

Eli Bagno, David Garber, Toufik Mansour, Robert Shwartz

Research output: Contribution to journalArticlepeer-review


The excedance number for Sn is known to have an Eulerian distribution. Nevertheless, the classical proof uses descents rather than excedances. We present a direct proof based on a recursion which uses only excedances and extend it to the flag-excedance parameter defined on the group of colored permutations Gr,n = ℤr ≀ Sn. We have also computed the distribution of a variant of the flag-excedance number, and show that its enumeration uses the Stirling number of the second kind. Moreover, we show that the generating function of the flag-excedance number defined on ℤr ≀ Sn is symmetric, and its variant is log-concave on ℤr ≀ Sn..
Original languageEnglish
Pages (from-to)1-18
Number of pages18
JournalPure Mathematics and Applications
Issue number1
StatePublished - 2015


Dive into the research topics of 'Recursions for the flag-excedance number in colored permutations groups'. Together they form a unique fingerprint.

Cite this