1503.03164Mar 11, 201518 pages, comments welcome; new material added regarding the limit of Frobenius complexity as p goes to infinity and connections to the Perron-Frobenius theorem. arXiv admin note: text overlap with arXiv:1401.0234

On the Frobenius complexity of determinantal rings

Florian Enescu, Yongwei Yao

Commutative Algebra

arXiv PDF

Abstract

We compute the Frobenius complexity for the determinantal ring of prime characteristic $p$ obtained by modding out the $2 \times 2$ minors of an $m \times n$ matrix of indeterminates, where $m > n \ge 2$

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. We also show that, as

p \to \infty

, the Frobenius complexity approaches

m-1

.

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