Even and odd compositions with restricted parts
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916236833587200 |
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| author | Huang, Jia |
| author_facet | Huang, Jia |
| contents | A result of Legendre asserts that the difference between the numbers of (length) even and odd partitions of $n$ into distinct parts is $0$, $1$, or $-1$; this also follows from Euler's pentagonal number theorem. We establish an analogous result for compositions and obtain some generalizations that are related to various entries in the On-Line Encyclopedia of Integer Sequences. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_03477 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Even and odd compositions with restricted parts Huang, Jia Combinatorics 05A15, 05A19 A result of Legendre asserts that the difference between the numbers of (length) even and odd partitions of $n$ into distinct parts is $0$, $1$, or $-1$; this also follows from Euler's pentagonal number theorem. We establish an analogous result for compositions and obtain some generalizations that are related to various entries in the On-Line Encyclopedia of Integer Sequences. |
| title | Even and odd compositions with restricted parts |
| topic | Combinatorics 05A15, 05A19 |
| url | https://arxiv.org/abs/2405.03477 |