On determinants of random symmetric matrices over Zm

101. R. P. Brent and B. D. McKay, On determinants of random symmetric matrices over Zm , Proceedings Second International Conference on Combinatorial Mathematics and Computing (edited by B. D. McKay), Ars Combinatoria 26A (1988), 57-64. MR 90g:05015, 89j:05001.

Also Technical Report TR-CS-88-03, February 1988 (republished October 1998), 8 pp. arXiv:1004.5440v1

Abstract: dvi (2K), pdf (27K), ps (25K).

Technical Report: dvi (14K), pdf (146K), ps (61K).

Abstract

We determine the probability that a random n × n symmetric matrix over {1, 2, ... , m} has determinant divisible by m.

Comments

For related work on random unsymmetric matrices, see [94].

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