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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- Masthead
- Distance-regular graph with the intersection array {45, 30, 7; 1, 2, 27} does not exist
- The impact of the growth rate of the packing number of graphs on the computational complexity of the independent set problem
- Traveling salesman polytopes and cut polytopes. Affine reducibility
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- Cycle structure of power mappings in a residue classes ring
- A criterion for the automata realizable functions to be boundedly deterministic
- On the complexity of two-dimensional discrete logarithm problem in a finite cyclic group with effective automorphism of order
- The completeness criterion for some systems containing P-sets of automaton functions
- On the synthesis of circuits admitting complete fault detection test sets of constant length under arbitrary constant faults at the outputs of the gates
- Factorially solvable rings
- Identities with permutations and quasigroups isotopic to groups and to Abelian groups
- Classes of projectively equivalent quadrics over local rings
