A Product Formula for Partition-Restricted Boundary Hypermatrix Counts
We prove the Koprowski--Lewis product conjecture for nondegenerate $2\times(k+1)\times k$ hypermatrices over finite fields with two partition-shaped layers of prescribed zeros. The result holds for every positive $k$, every finite field, and every admissible pair of partitions. After fixing the first slice, nondegeneracy is equivalent to simplicity of a partial linear map. Applying the simple-extension theorem of Arora, Ram, and Venkateswarlu inside the successive allowed row spaces gives the product directly. We include an elementary proof of that extension theorem and justify the…
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