A Generalized Burge Correspondence and $k$-measure of Partitions
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866912008436187136 |
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| author | Irving, John |
| author_facet | Irving, John |
| contents | Let $P$ be the set of integer partitions and $D$ the subset of those with distinct parts. We extend a correspondence of Burge between partitions and binary words to give encodings of both $D$ and $D$ as words over a $k$-ary alphabet, for any fixed $k\geq 2$. These are used to prove refinements of two partition identities involving $k$-measure that were recently derived algebraically by Andrews, Chern and Li. The relationship between our encoding of $D$ and minimum gap-size partition identities (e.g. Schur's Theorem) is also briefly discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_16910 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Generalized Burge Correspondence and $k$-measure of Partitions Irving, John Combinatorics 05A17 (Primary) 05A19, 05A30, 11P81 (Secondary) Let $P$ be the set of integer partitions and $D$ the subset of those with distinct parts. We extend a correspondence of Burge between partitions and binary words to give encodings of both $D$ and $D$ as words over a $k$-ary alphabet, for any fixed $k\geq 2$. These are used to prove refinements of two partition identities involving $k$-measure that were recently derived algebraically by Andrews, Chern and Li. The relationship between our encoding of $D$ and minimum gap-size partition identities (e.g. Schur's Theorem) is also briefly discussed. |
| title | A Generalized Burge Correspondence and $k$-measure of Partitions |
| topic | Combinatorics 05A17 (Primary) 05A19, 05A30, 11P81 (Secondary) |
| url | https://arxiv.org/abs/2408.16910 |