Vol. 300, No. 2, 2019

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

Doowon Koh, Thang Pham, Chun-Yen Shen and Le Anh Vinh

Vol. 300 (2019), No. 2, 405–417

Let A be a set in a prime field Fp. We prove that d × d matrices with entries in A determine almost |A|3+ 1 45 distinct determinants and almost |A|21 6 distinct permanents when |A| is small enough. Our proofs rely on recent advances in additive combinatorics and incidence machinery.

finite fields, sum-product estimates, determinant, permanent, matrix
Mathematical Subject Classification 2010
Primary: 05C50
Received: 1 January 2018
Revised: 25 September 2018
Accepted: 25 September 2018
Published: 30 July 2019
Doowon Koh
Department of Mathematics
Chungbuk National University
Cheongju City
South Korea
Thang Pham
Department of Mathematics
University of California, San Diego
La Jolla, CA
United States
Chun-Yen Shen
Department of Mathematics
National Taiwan University
Le Anh Vinh
University of Education
Vietnam Institute of Educational Sciences
Cau Giay
Hanoi 100000