Rectangle partitions generalizing integer partitions
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916981325692928 |
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| author | Gajdzica, Krystian Visser, Robin Zakarczemny, Maciej |
| author_facet | Gajdzica, Krystian Visser, Robin Zakarczemny, Maciej |
| contents | In this paper, we introduce a natural geometric extension of the partition function. More precisely, we investigate the problem of counting partitions of a rectangle into rectangular blocks with integer sides. Here, two partitions of a rectangle are indistinguishable if they consist of the same multiset of blocks, their geometric arrangement does not matter. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_20495 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rectangle partitions generalizing integer partitions Gajdzica, Krystian Visser, Robin Zakarczemny, Maciej Combinatorics Number Theory 05A16, 11P81 (Primary) 05A15, 11P83 (Secondary) In this paper, we introduce a natural geometric extension of the partition function. More precisely, we investigate the problem of counting partitions of a rectangle into rectangular blocks with integer sides. Here, two partitions of a rectangle are indistinguishable if they consist of the same multiset of blocks, their geometric arrangement does not matter. |
| title | Rectangle partitions generalizing integer partitions |
| topic | Combinatorics Number Theory 05A16, 11P81 (Primary) 05A15, 11P83 (Secondary) |
| url | https://arxiv.org/abs/2509.20495 |