A combinatorial proof of the log-concavity of the numbers of permutations with k runs

Authors
Bona, M Ehrenborg, R
Citation
M. Bona et R. Ehrenborg, A combinatorial proof of the log-concavity of the numbers of permutations with k runs, J COMB TH A, 90(2), 2000, pp. 293-303
Citations number
7
Categorie Soggetti
Mathematics
Journal title
JOURNAL OF COMBINATORIAL THEORY SERIES A
ISSN journal
00973165 → ACNP
Volume
90
Issue
2
Year of publication
2000
Pages
293 - 303
Database
ISI
SICI code
0097-3165(200005)90:2<293:ACPOTL>2.0.ZU;2-M
Abstract
We combinatorially prove that the number R(n, k) of permutations of length n having it runs is a log-concave sequence in k, for all n. We also give a new combinatorial proof for the log-concavity of the Eulerian numbers. (C) 2000 Academic Press.