Latin cubes with disjoint subcubes of two orders
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911542175334400 |
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| author | Kemp, Tara Lefevre, James G. |
| author_facet | Kemp, Tara Lefevre, James G. |
| contents | Given a partition $h_1+h_2+\dots+h_k = n$, a latin square of order $n$ with pairwise disjoint subsquares of orders $h_1,\dots ,h_k$ is called a realization. When the values $h_i$ are of at most two sizes, the existence of a realization has been completely determined. However, the existence of a latin cube with pairwise disjoint subcubes of two orders is only partially solved. In this paper, we determine existence for such latin cubes in almost all cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_06768 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Latin cubes with disjoint subcubes of two orders Kemp, Tara Lefevre, James G. Combinatorics Given a partition $h_1+h_2+\dots+h_k = n$, a latin square of order $n$ with pairwise disjoint subsquares of orders $h_1,\dots ,h_k$ is called a realization. When the values $h_i$ are of at most two sizes, the existence of a realization has been completely determined. However, the existence of a latin cube with pairwise disjoint subcubes of two orders is only partially solved. In this paper, we determine existence for such latin cubes in almost all cases. |
| title | Latin cubes with disjoint subcubes of two orders |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2511.06768 |