A Generalized Burge Correspondence and $k$-measure of Partitions
| Autor: | Irving, John |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 27 pages, 5 figures |
| Databáze: | arXiv |
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