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An Eulerian permutation statistic and generalizations

By Travis Hance and Nan Li

Abstract

Recently, the second author studied an Eulerian statistic (called cover) in the context of convex polytopes, and proved an equal joint distribution of (cover,des) with (des,exc). In this paper, we present several direct bijective proofs that cover is Eulerian, and examine its generalizations and their Mahonian partners. We also present a quasi-symmetric function proof (suggested by Michelle Wachs) of the above equal joint distribution

Topics: Mathematics - Combinatorics, 05A19(Primary) 05A05, 05E05 (Secondary)
Year: 2012
OAI identifier: oai:arXiv.org:1208.3063

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