Hostname: page-component-848d4c4894-ttngx Total loading time: 0 Render date: 2024-06-01T19:23:32.275Z Has data issue: false hasContentIssue false
  • English
  • Français

Algebras of Acyclic Type

Published online by Cambridge University Press:  20 November 2018

Phil Hanlon
Phil Hanlon*
Affiliation:
Cal Tech, Pasadena, California
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 33 , Issue 1 , 01 February 1981 , pp. 129 - 141
Copyright
Copyright © Canadian Mathematical Society 1981

References

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. Robinson, R. W., Counting labelled acyclic digraphs, in New directions in the theory of graphs (Academic Press, New York, 1973), 239–273.Google Scholar
3. Rota, G. C., On the foundations of combinatorial theory I. Theory of Mobius functions, Z. Wahrscheinlichkeits théorie und Verw. Gebiete 2 (1964), 340–368.Google Scholar
4. Stanley, R. P., Acyclic orientations of graphs, Discrete Math. 5 (1973), 171–178.Google Scholar