Enumeration of nondegenerate 2x(k+1)xk hypermatrices
Abstract
We consider the problem of enumerating hypermatrices of format 2 × (k + 1) × 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.
Fields of Study & Subjects
Advanced Combinatorial Mathematics
Advanced Mathematical Identities
Tensor decomposition and applications
Publication details
- Journal / source
- Enumerative Combinatorics and Applications
- Volume
- 7
- Issue
- 1
- Pages
- Article #S2R3–Article #S2R3
- Publication date
- 31 July 2026
- Language
- EN