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Simple proof of a theorem on permanents

Published online by Cambridge University Press:  18 May 2009

D. Ž. Djoković
D. Ž. Djoković
Affiliation:
Faculty of Mathematics, University of Waterloo, Waterloo, Ontario, Canada
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Let A = (aij) be an n × n complex matrix. The permanent of this matrix is

where the sum is taken over all permutations p of the set {1, …, n}.

In a recent paper [1] E. H. Lieb proved an interesting theorem (see below) which he applied to verify some conjectures of M. Marcus and M. Newman. The purpose of this note is to give a simple proof of Lieb's theorem.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 10 , Issue 1 , January 1969 , pp. 52 - 54
Copyright
Copyright © Glasgow Mathematical Journal Trust 1969

References

REFERENCES

1.Lieb, E. H., Proofs of some conjectures on permanents, J. Mech. Math. 16 (1966), 127–134.Google Scholar