Graphs of Reduced Words and Some Connections
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866913391136735232 |
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| author | Adeyemo, Praise |
| author_facet | Adeyemo, Praise |
| contents | The family of graphs of reduced words of a certain subcollection of permutations in the union $\cup_{n\geq 4}\frak{S}_{n}$ of symmetic groups is investigated. The subcollection is characterised by the hook cycle type $(n-2,1,1)$ with consecutive fixed points. A closed formula for counting the vertices of each member of the family is given and the vertex-degree polynomials for the graphs with their generating series is realised. Lastly, some isomorphisms of these graphs with various combinatorial objects are established. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_09666 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Graphs of Reduced Words and Some Connections Adeyemo, Praise Combinatorics The family of graphs of reduced words of a certain subcollection of permutations in the union $\cup_{n\geq 4}\frak{S}_{n}$ of symmetic groups is investigated. The subcollection is characterised by the hook cycle type $(n-2,1,1)$ with consecutive fixed points. A closed formula for counting the vertices of each member of the family is given and the vertex-degree polynomials for the graphs with their generating series is realised. Lastly, some isomorphisms of these graphs with various combinatorial objects are established. |
| title | Graphs of Reduced Words and Some Connections |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2406.09666 |