Abstract
Let Δn be the set of all n × n, non-singular matrices of the form PD, where P is a permutation matrix and D is a diagonal matrix with complex entries. In (1, conjecture 12), Marcus and Mine asked: Is Δn a maximal group on which the permanent function is multiplicative? (that is, per AB = per A per B). The field over which the entries range was not mentioned in the conjecture; however, we assume that the complex number field was intended. Corollary 1 answers this in the affirmative. In fact, Δn is the only maximal group (or semigroup) on which the permanent is multiplicative. Let ρi be the set of all non-zero entries in the ith row and let λj be the set of all non-zero entries in the jth column.
Publisher
Canadian Mathematical Society
Cited by
5 articles.
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