Zero-sum square matrices

Paul Balister, Yair Caro, Cecil Rousseau, Raphael Yuster

Research output: Contribution to journalArticlepeer-review


Let A be a matrix over the integers, and let p be a positive integer. A submatrix B of A is zero-sum mod p if the sum of each row of B and the sum of each column of B is a multiple of p. Let M(p, k) denote the least integer in for which every square matrix of order at least m has a square submatrix of order k which is zero-sum mod p. In this paper we supply upper and lower bounds for M(p, k). In particular, we prove that lim sup M(2, k)/k ≤ 4, lim inf M(3, k)/k ≤ 20, and that M(p, k) ≥ k√2/2e exp(1/e)p/2. Some nontrivial explicit values are also computed.

Original languageEnglish
Pages (from-to)489-497
Number of pages9
JournalEuropean Journal of Combinatorics
Issue number5
StatePublished - Jul 2002

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics


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