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On the Möbius function of Hom(P, Q)

Published online by Cambridge University Press:  17 April 2009

T.P. Speed
Affiliation:
Division of Mathematics and Statistics, CSIRO, GPO Box 1965, Canberra, ACT 2601, Australia.
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Abstract

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A formula is given for the Möbius function of the poset Hom(P, Q) of all order-preserving maps between two finite posets P and Q. Two applications of the formula are presented.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1984

References

[1]Aigner, Martin, Combinatorial theory (Die Grundlehren der mathematischen Wissenschaften, 234. Springer-Verlag, Berlin, Heidelberg, New York, 1979).CrossRefGoogle Scholar
[2]Bailey, R.A., Praeger, Cheryl E., Rowley, C.A. and Speed, T.P., “Generalized wreath products of permutation groups”, Proc. London Math. Soc. (3) 47 (1983), 6982.CrossRefGoogle Scholar
[3]Birkhoff, Garrett, Lattice theory, Third Edition (American Mathematical Society Colloquium Publications, 25. American Mathematical Society, Providence, Rhode Island, 1967).Google Scholar
[4]Doubilet, Peter, “On the foundations of combinatorial theory VII: symmetric functions through the theory of distribution and occupancy”, Stud. Appl. Math. 51 (1972), 377396.CrossRefGoogle Scholar
[5]Praeger, Cheryl E., Rowley, C.A. and Speed, T.P., “A note on generalised wreath product groups”, submitted.Google Scholar
[6]Rota, Gian-Carlo, “On the foundations of combinatorial theory I. Theory of Möbius functions”, Z. Wahrsch. Verw. Gebiete 2 (1963/1964), 340368.CrossRefGoogle Scholar
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