Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4653352 | European Journal of Combinatorics | 2016 | 23 Pages |
Abstract
We consider several generalizations of the classical γγ-positivity of Eulerian polynomials (and their derangement analogues) using generating functions and combinatorial theory of continued fractions. For the symmetric group, we prove an expansion formula for inversions and excedances as well as a similar expansion for derangements. We also prove the γγ-positivity for Eulerian polynomials for derangements of type BB. More general expansion formulae are also given for Eulerian polynomials for rr-colored derangements. Our results answer and generalize several recent open problems in the literature.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Heesung Shin, Jiang Zeng,