Zero-sum Square Matrices

✍ Scribed by Paul Balister; Yair Caro; Cecil Rousseau; Raphael Yuster

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 94 KB
• Volume: 23
• Category: Article
• ISSN: 0195-6698
• DOI: 10.1006/eujc.2002.0595

✦ Synopsis

Let A be a matrix over the integers, and let p be a positive integer. A submatrix B of A is zerosum 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 m 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

2e exp(1/e) p/2 . Some nontrivial explicit values are also computed.