Title

The structure of the consecutive pattern poset

Publication Date

2018

Journal

International Mathematics Research Notices

Volume

2018

Issue

7

First Page

2099

Last Page

2134

Department

Mathematics

Abstract

The consecutive pattern poset is the infinite partially ordered set of all permutations where σ ≤ τ if τ has a subsequence of adjacent entries in the same relative order as the entries of σ. We study the structure of the intervals in this poset from topological, poset-theoretic, and enumerative perspectives. In particular, we prove that all intervals are rank-unimodal and strongly Sperner, and we characterize disconnected and shellable intervals. We also show that most intervals are not shellable and have Möbius function equal to zero.

Comments

12 month embargo period from date published online, January 8, 2017.

DOI

doi: 10.1093/imrn/rnw293

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