On the determinants and permanents of matrices with restricted entries over prime fields

Authors: Doowon Koh, Phạm Văn Thắng, Chun-Yen Shen, Lê Anh Vinh,

https://doi.org/10.2140/pjm.2019.300.405

Publisher, magazine: ,

Publication year: 2019

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Abstract

Let A be a set in a prime field F p . We prove that d × d matrices with entries in A determine almost ∣ ∣ A ∣ ∣ 3 + 1 4 5 distinct determinants and almost ∣ ∣ A ∣ ∣ 2 − 1 6 distinct permanents when | A | is small enough. Our proofs rely on recent advances in additive combinatorics and incidence machinery.

Tags: finite fields, sum-product estimates, determinant, permanent, matrix