Minors of the constraint matrix in multi-index transport problems
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E. B. Titova
Abstract
For a constraint matrix Ts,k(n) of the k-index s-ary transport problem, where each index takes n values, we consider behavior of the function αj(Ts,k(n)) being equal to the mean value of square of αjth order minor of the matrix Ts,k(n). Two-sided estimates of the logarithm of αj(Ts,k(n)) are established. On this base, classification values j such that αj(Ts,k(n))) tends to infinity and such that αj(Ts,k(n)) tends to zero is obtained. An estimate of the maximal value of minors of the matrix Ts,k(n) is given. Asymptotics of the function αA(Ts,k(n)) being equal to the mean value of square of the minor constructed on the basis system of rows of matrix Ts,k(n) is found. Main part of these results was announced earlier without proofs.
The work was supported by the Russian Foundation for Basic Research, project 09-01- 00545-a.
© 2014 by Walter de Gruyter GmbH & Co.
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