The Rearrangement Conjecture

The Rearrangement Conjecture states that if two words over $\mathbb{P}$ are Wilf-equivalent in the factor order on $\mathbb{P}^{\ast}$ then they are rearrangements of each other. We introduce the notion of strong Wilf-equivalence and prove that if two words over $\mathbb{P}$ are strongly Wilf-equiva...

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Bibliographic Details
Published inDiscrete Mathematics and Theoretical Computer Science Vol. DMTCS Proceedings vol. AT,...; no. Proceedings; pp. 217 - 228
Main Authors Pantone, Jay, Vatter, Vincent
Format Journal Article Conference Proceeding
LanguageEnglish
Published DMTCS 01.01.2014
Discrete Mathematics and Theoretical Computer Science
Discrete Mathematics & Theoretical Computer Science
SeriesDMTCS Proceedings
Subjects
[info.info-dm] computer science [cs]/discrete mathematics [cs.dm]
[math.math-co] mathematics [math]/combinatorics [math.co]
Combinatorics
composition
Computer Science
Discrete Mathematics
generalized factor order
Mathematics
wilf-equivalence
Wilf-equivalence
composition
generalized factor order
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Summary:The Rearrangement Conjecture states that if two words over $\mathbb{P}$ are Wilf-equivalent in the factor order on $\mathbb{P}^{\ast}$ then they are rearrangements of each other. We introduce the notion of strong Wilf-equivalence and prove that if two words over $\mathbb{P}$ are strongly Wilf-equivalent then they are rearrangements of each other. We further conjecture that Wilf-equivalence implies strong Wilf-equivalence.
ISSN:1365-8050
1462-7264
1365-8050
DOI:10.46298/dmtcs.2394