
Accession Number : ADA182264
Title : Matrix Theory.
Descriptive Note : Annual rept. 1 Jul 8630 Jun 87,
Corporate Author : CALIFORNIA UNIV SANTA BARBARA DEPT OF MATHEMATICS
Personal Author(s) : Minc, Henryk
PDF Url : ADA182264
Report Date : 30 Jun 1987
Pagination or Media Count : 5
Abstract : Two areas of matrix theory are discussed: the theory of permanents, and the theory of nonnegative matrices. Paper (1) deals with permanental compounds and their use in recurrence formulas for permanents of (0,1)circulants and in related asymptotic formulas. Paper (2) is a extensive survey of the progress in the theory of permanents achieved during the quadrennium 19821985. Paper (3) deals with the problem of determining the minimum permanent in the set of n x n doubly stochastic matrices whose first main diagonal entries are equal to zero. The case k = o is the famed van der Waerden conjecture. The case k = 1 can be easily solved by a method similar to that used by Egorycev in proving the van der Waerden conjecture. For k = 2 Egorycev's techniques are of limited use. The case was solved by me in 1984. For 3 or  n the problem is still unsolved.
Descriptors : *MATRIX THEORY, ASYMPTOTIC SERIES
Subject Categories : Theoretical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE