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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Enumeration of posets generated by disjoint unions and ordinal sums


Author: Richard P. Stanley
Journal: Proc. Amer. Math. Soc. 45 (1974), 295-299
MSC: Primary 06A10
MathSciNet review: 0351928
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Abstract: Let $ {f_n}$ be the number of $ n$-element posets which can be built up from a given collection of finite posets using the operations of disjoint union and ordinal sum. A curious functional equation is obtained for the generating function $ \Sigma {f_n}{x^n}$. Using a result of Bender, an asymptotic estimate can sometimes be given for $ {f_n}$. The analogous problem for labeled posets is also considered.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1974-0351928-7
PII: S 0002-9939(1974)0351928-7
Keywords: Poset, partially ordered set, disjoint union, ordinal sum, generating function, Pólya's enumeration theorem, functional equation
Article copyright: © Copyright 1974 American Mathematical Society