<abstract xmlns="http://www.w3.org/1999/xhtml"> 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.. </abstract>

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..

Recursions for the flag-excedance number in colored permutations groups

The Jerusalem College of Technology 93721 Jerusalem, Israel

Department of Applied Mathematics Holon Institute of Technology 58102 Holon, Israel

Department of Mathematics University of Haifa 31905 Haifa, Israel

Department of Computer Sciences and Mathematics Ariel University 40700 Ariel, Israel

Pure Mathematics and Applications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"Recursions for the flag-excedance number in colored permutations groups"}

The excedance number for Sn is known to have an Eulerian distribution. Nevertheless, the classical proof uses descents rather than excedances. We present a...

Recursions for the flag-excedance number in colored permutations groups

Published Online: Oct 07, 2015

Page range: 1 - 18

Received: Nov 15, 2014

DOI: https://doi.org/10.1515/puma-2015-0005

Keywords
colored permutation group, flag-excedance number, Stirling number of second kind, permutation statistics, recursion

© 2015

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Recursions for the flag-excedance number in colored permutations groups

Published Online: Oct 07, 2015

Page range: 1 - 18

Received: Nov 15, 2014

DOI: https://doi.org/10.1515/puma-2015-0005

Keywordscolored permutation group, flag-excedance number, Stirling number of second kind, permutation statistics, recursion

© 2015

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
colored permutation group, flag-excedance number, Stirling number of second kind, permutation statistics, recursion