The permanent of a transitive relation
Author:
Henry Sharp
Journal:
Proc. Amer. Math. Soc. 26 (1970), 153-157
MSC:
Primary 15.20
DOI:
https://doi.org/10.1090/S0002-9939-1970-0279111-0
MathSciNet review:
0279111
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Abstract: H. Minc has constructed an upper bound on the permanent of any relation on a finite set. In this paper the permanent of any transitive relation on a finite set is calculated. The work in part is based upon the interpretation of a reflexive, transitive relation as a finite topology. The relationship to (finite) Borel fields is discussed briefly. In an example it is shown how results here may be combined with Mincβs inequality to produce an improved upper bound on the permanent of any relation.
- Henryk Minc, Upper bounds for permanents of $(0,\,1)$-matrices, Bull. Amer. Math. Soc. 69 (1963), 789β791. MR 155843, DOI https://doi.org/10.1090/S0002-9904-1963-11031-9
- Henryk Minc, An inequality for permanents of $(0,\,1)-matrices.$, J. Combinatorial Theory 2 (1967), 321β326. MR 211890
- Marlon Rayburn, On the Borel fields of a finite set, Proc. Amer. Math. Soc. 19 (1968), 885β889. MR 227034, DOI https://doi.org/10.1090/S0002-9939-1968-0227034-6
- Henry Sharp Jr., Quasi-orderings and topologies on finite sets, Proc. Amer. Math. Soc. 17 (1966), 1344β1349. MR 217771, DOI https://doi.org/10.1090/S0002-9939-1966-0217771-X
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Keywords:
Permanent of <IMG WIDTH="50" HEIGHT="41" ALIGN="MIDDLE" BORDER="0" SRC="images/img3.gif" ALT="$(0,1)$">-matrix,
relations on finite sets,
transitive relations,
finite topologies,
finite Borel fields
Article copyright:
© Copyright 1970
American Mathematical Society