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The incidence algebra of a group reduced partially ordered set

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Part of the Lecture Notes in Mathematics book series (LNM,volume 829)

Abstract

Let (P,⩽) be a locally finite partially ordered set with no infinite descending chains, let G be a finite subgroup of the automorphism group of P and let P(G) be the set of orbits of P under the action of G. Define a partial ordering ⩽G on P(G) by saying that an orbit A is less than or equal to an orbit B if there exist elements a ε A and b ε B with a⩽b. We show that I (P(G)), the incidence algebra of P(G), is the homomorphic image of a subalgebra of I(P) via a Polya-type homomorphism. We compute a natural inverse image for each function of I(P(G)) and in particular for the Möbius function of P(G).

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Reference

  1. G.C. Rota, On the foundations of combinatorial theory I. Theory of Möbius Functions, Z. Wahrsch. Verw. Gebiete 2 (1964), 340–368.

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© 1980 Springer-Verlag

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Hanlon, P. (1980). The incidence algebra of a group reduced partially ordered set. In: Robinson, R.W., Southern, G.W., Wallis, W.D. (eds) Combinatorial Mathematics VII. Lecture Notes in Mathematics, vol 829. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0088908

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  • DOI: https://doi.org/10.1007/BFb0088908

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10254-0

  • Online ISBN: 978-3-540-38376-5

  • eBook Packages: Springer Book Archive