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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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2014-01-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
| Subjects: | |
| Online Access: | https://dmtcs.episciences.org/2394/pdf |
| _version_ | 1797270292731527168 |
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| author | Jay Pantone Vincent Vatter |
| author_facet | Jay Pantone Vincent Vatter |
| author_sort | Jay Pantone |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-25T02:01:57Z |
| format | Article |
| id | doaj.art-8a5d9199235843c6b573e0b38bbbdcfa |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:01:57Z |
| publishDate | 2014-01-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-8a5d9199235843c6b573e0b38bbbdcfa2024-03-07T14:53:18ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502014-01-01DMTCS Proceedings vol. AT,...Proceedings10.46298/dmtcs.23942394The Rearrangement ConjectureJay Pantone0Vincent Vatter1Department of Mathematics [Gainesville]Department of Mathematics [Gainesville]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.https://dmtcs.episciences.org/2394/pdfcompositiongeneralized factor orderwilf-equivalence[info.info-dm] computer science [cs]/discrete mathematics [cs.dm][math.math-co] mathematics [math]/combinatorics [math.co] |
| spellingShingle | Jay Pantone Vincent Vatter The Rearrangement Conjecture Discrete Mathematics & Theoretical Computer Science composition generalized factor order wilf-equivalence [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] [math.math-co] mathematics [math]/combinatorics [math.co] |
| title | The Rearrangement Conjecture |
| title_full | The Rearrangement Conjecture |
| title_fullStr | The Rearrangement Conjecture |
| title_full_unstemmed | The Rearrangement Conjecture |
| title_short | The Rearrangement Conjecture |
| title_sort | rearrangement conjecture |
| topic | composition generalized factor order wilf-equivalence [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] [math.math-co] mathematics [math]/combinatorics [math.co] |
| url | https://dmtcs.episciences.org/2394/pdf |
| work_keys_str_mv | AT jaypantone therearrangementconjecture AT vincentvatter therearrangementconjecture AT jaypantone rearrangementconjecture AT vincentvatter rearrangementconjecture |