On the Slice Rank of Tensors in P-Echelon Form

2026/07/21 by Omran Ahmadi, Hassan Norouzi
#math.CO #math.RA

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Abstract

For a totally ordered finite set A with the total order Q, a poset P=([d],≤_P), and a field \mathbbF, a tensor T:A^d\longrightarrow \mathbbF is in P-echelon form if r≤_Ps in P implies a_r≤_Q a_s in every tuple (a₁,…,a_d) in the support of T. We prove that if the Hasse diagram of P has no isolated vertex, then tensors in P-echelon form with nonzero diagonal entries have full slice-rank. Our results extend and improve on recent results of Amanov and Yeliussizov.

Citations

• Tensor slice rank and Cayley's first hyperdeterminant

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