ConsecutivePatterns.pdf

Peter R. W. McNamara; Sergi Elizalde

doi:10.1093/imrn/rnw293

ConsecutivePatterns.pdf

Peter R. W. McNamara
, Sergi Elizalde

Bucknell University

Dartmouth College

Research output: Contribution to journal › Article › peer-review

Abstract

The consecutive pattern poset is the infinite partially ordered set of all permutations where sigma < tau if \tau has a subsequence of adjacent entries in the same relative order as the entries of sigma. 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.

Original language	American English
Journal	International Mathematics Reseach Notices
Volume	2018
DOIs	https://doi.org/10.1093/imrn/rnw293
State	Published - Feb 6 2018

Keywords

Consecutive pattern
poset
disconnected
shellable
rank unimodal
Sperner
exterior
Möbius function

Disciplines

Mathematics

Access to Document

10.1093/imrn/rnw293License: Unspecified

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Cite this

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title = "ConsecutivePatterns.pdf",

abstract = " The consecutive pattern poset is the infinite partially ordered set of all permutations where sigma < tau if \textbackslash{}tau has a subsequence of adjacent entries in the same relative order as the entries of sigma. 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 M{\"o}bius function equal to zero.",

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AB - The consecutive pattern poset is the infinite partially ordered set of all permutations where sigma < tau if \tau has a subsequence of adjacent entries in the same relative order as the entries of sigma. 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.

KW - Consecutive pattern

KW - poset

KW - disconnected

KW - shellable

KW - rank unimodal

KW - Sperner

KW - exterior

KW - Möbius function

U2 - 10.1093/imrn/rnw293

DO - 10.1093/imrn/rnw293

M3 - Article

VL - 2018

JO - International Mathematics Reseach Notices

JF - International Mathematics Reseach Notices

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