Interlacing log-concavity of the derangement polynomials and the Eulerian polynomials

Let D(n,k) be the set of derangements of [n] with k excedances and d(n,k) be the cardinality of D(n,k). We establish a bijection between D(n,k) and the set of labeled lattice paths of length n with k horizontal edges. Using this bijection, we give a direct combinatorial proof of the inequalities d(n...

Full description

Saved in:
Bibliographic Details
Published in:European journal of combinatorics 2016-11, Vol.58, p.52-60
Main Authors: Gu, Cindy C.Y., Wang, Larry X.W.
Format: Article
Language:English
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Let D(n,k) be the set of derangements of [n] with k excedances and d(n,k) be the cardinality of D(n,k). We establish a bijection between D(n,k) and the set of labeled lattice paths of length n with k horizontal edges. Using this bijection, we give a direct combinatorial proof of the inequalities d(n,k−1)d(m,l+1)
ISSN:0195-6698
1095-9971
DOI:10.1016/j.ejc.2016.04.009