Enumeration of Nondegenerate $2 \times (k+1) \times k$ Hypermatrices
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866908852517076992 |
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| author | Koprowski, Brandon Lewis, Joel Brewster |
| author_facet | Koprowski, Brandon Lewis, Joel Brewster |
| contents | We consider the problem of enumerating hypermatrices of format $2 \times (k + 1) \times k$ over a finite field that have nonzero hyperdeterminant and whose nonzero entries are restricted to a plane partition. We conjecture an attractive product formula for the enumeration, and prove it in many cases. In general, we show that the enumeration is given (up to a power of $q - 1$) by a polynomial in $q$ with nonnegative integer coefficients, whose value at $q = 1$ enumerates a natural family of three-dimensional rook placements. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_22129 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Enumeration of Nondegenerate $2 \times (k+1) \times k$ Hypermatrices Koprowski, Brandon Lewis, Joel Brewster Combinatorics We consider the problem of enumerating hypermatrices of format $2 \times (k + 1) \times k$ over a finite field that have nonzero hyperdeterminant and whose nonzero entries are restricted to a plane partition. We conjecture an attractive product formula for the enumeration, and prove it in many cases. In general, we show that the enumeration is given (up to a power of $q - 1$) by a polynomial in $q$ with nonnegative integer coefficients, whose value at $q = 1$ enumerates a natural family of three-dimensional rook placements. |
| title | Enumeration of Nondegenerate $2 \times (k+1) \times k$ Hypermatrices |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2602.22129 |