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On the Conversion of the Determinant into the Permanent

Published online by Cambridge University Press:  20 November 2018

Peter Botta
Peter Botta*
Affiliation:
University of Michigan and University of Toronto
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Let Mm(F) be the vector space of m - square matrices over a field F. If X belongs to Mm(F), then xij will denote the element occuring in row i and column j of X.

Let Sm be the symmetric group of degree m and ε: Sm → F the alternating character on Sm (i.e. ε(σ) = 1 or - 1 according as σ is an even or odd permutation).

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 11 , Issue 1 , April 1968 , pp. 31 - 34
Copyright
Copyright © Canadian Mathematical Society 1968

References

1. Botta, Peter, Linear Transformations that preserve the Permanent, to appear in Proc. Amer. Math. Soc. Google Scholar
2. Marcus, M., Linear Operations on Matrices, Amer. Math. Monthly, 69 (1962), 837-847.10.1080/00029890.1962.11989991Google Scholar
3. Marcus, M. and May, F., The Permanent Function, Canad. J. Math. 14 (1962), 177-189.10.4153/CJM-1962-013-4Google Scholar
4. Marcus, M. and Mine, H., On the Relation between the Permanent and the Determinant, Illinois J. Math., 5 (1961), 376-381.10.1215/ijm/1255630882Google Scholar
5. Marcus, M. and Moyls, B.N., Linear Transformations on Algebras of Matrices, Canad. J. Math., 11(1959), 61-66.10.4153/CJM-1959-008-0Google Scholar
6. Polya, G., Aufgabe 424, Arch. Math. u. Phys., 20, p. 271.Google Scholar