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The semigroup of doubly-stochastic matrices

Published online by Cambridge University Press:  18 May 2009

H. K. Farahat
H. K. Farahat
Affiliation:
The University, Sheffield
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The set Dn of all n × n doubly-stochastic matrices is a semigroup with respect to ordinary matrix multiplication. This note is concerned with the determination of the maximal subgroups of Dn. It is shown that the number of subgroups is finite, that each subgroup is finite and is in fact isomorphic to a direct product of symmetric groups. These results are applied in § 3 to yield information about the least number of permutation matrices whose convex hull contains a given doubly-stochastic matrix.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 7 , Issue 4 , July 1966 , pp. 178 - 183
Copyright
Copyright © Glasgow Mathematical Journal Trust 1966

References

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