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
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
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