Latin hypercubes realizing integer partitions
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866909456639459328 |
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| author | Donovan, Diane Kemp, Tara Lefevre, James |
| author_facet | Donovan, Diane Kemp, Tara Lefevre, James |
| contents | For an integer partition $h_1 + \dots + h_n = N$, a 2-realization of this partition is a latin square of order $N$ with disjoint subsquares of orders $h_1,\dots,h_n$. The existence of 2-realizations is a partially solved problem posed by Fuchs. In this paper, we extend Fuchs' problem to $m$-ary quasigroups, or, equivalently, latin hypercubes. We construct latin cubes for some partitions with at most two distinct parts and highlight how the new problem is related to the original. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_10981 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Latin hypercubes realizing integer partitions Donovan, Diane Kemp, Tara Lefevre, James Combinatorics For an integer partition $h_1 + \dots + h_n = N$, a 2-realization of this partition is a latin square of order $N$ with disjoint subsquares of orders $h_1,\dots,h_n$. The existence of 2-realizations is a partially solved problem posed by Fuchs. In this paper, we extend Fuchs' problem to $m$-ary quasigroups, or, equivalently, latin hypercubes. We construct latin cubes for some partitions with at most two distinct parts and highlight how the new problem is related to the original. |
| title | Latin hypercubes realizing integer partitions |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2312.10981 |