Geodesic
Algebras of Acyclic Type
Canadian journal of mathematics, Tome 33 (1981) no. 1, pp. 129-141

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper we consider the problem of determining when an algebra of formal power series over a commutative ring R is the homomorphic image of a reduced incidence algebra P(R, ∽). The question of when two such algebras are isomorphic is answered in Section 8 of [1]. A slight generalization of their notion of full binomial type is introduced here.Section 1 contains background material together writh a summary of the results of [1]. In Section 2 we present the desired characterization, and to conclude an application appears in Section 3. In Section 3 the tools of Section 2 are used to derive an equation of R. W. Robinson and R. P. Stanley which counts labelled, acyclic digraphs. 
Hanlon, Phil. Algebras of Acyclic Type. Canadian journal of mathematics, Tome 33 (1981) no. 1, pp. 129-141. doi: 10.4153/CJM-1981-012-0
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[1] 1. Doubilet, P., Rota, G. C. and Stanley, R. P., On the foundations of combinatorial theory (VI): The idea ofgenerating functions, Proc. of the Sixth Berkeley Symp. on Math. Stat, and Prob. Volume II (1972), 267–318. Google Scholar

[2] 2. Robinson, R. W., Counting labelled acyclic digraphs, in New directions in the theory of graphs (Academic Press, New York, 1973), 239–273. Google Scholar

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[4] 4. Stanley, R. P., Acyclic orientations of graphs, Discrete Math. 5 (1973), 171–178. Google Scholar

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