ALGOIUTHM 361 PERMANENT FUNCTION OF A SQUARE MATRIX I AND II [G6} BnucE SHlUVER, P. J. EBERLEIN, AND R. D. DIXON (Reed. 1H Feb. 1969, 7 Mar. 1969 and 9 July 1969) Stltte University of New York at Buffalo, Amherst, NY 14~~(j KEY WORDS AND PHRASES: matrix, permanent, determi lIant CR CATEGORIES: 5.30 real proeedure perl (A, n) j integer nj array Aj comment Let A be an n X n real matrix, n > 1. The permanent function of A, denoted per(A), is computed by H. J. Ryser's  expansion formula: n-l per(A) = r=O L (_I)r II xETn_ri=l L T Xi where Tj, j = n, n - 1, ... ,2, 1, is the set of vectors x = (Xi), i = 1, 2, '" , n which are obtained by adding j columns of A together in au(;) possible ways. To effect the sum over vectors in T;, n - 1 sums are computed. The natural 1-1 map from the binary integers to all r-combinations, r = 1, 2, ... , n - 1, is used to increment the sums over the sets T;. REFERENCE: 1. RYSER, H. J. Combinatorial Mathematics, Carus Monograph #14. Wiley,
Communications of the ACM – acm
Published: Nov 1, 1969
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