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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Enumeration of posets generated by disjoint unions and ordinal sums
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by Richard P. Stanley
Proc. Amer. Math. Soc. 45 (1974), 295-299
DOI: https://doi.org/10.1090/S0002-9939-1974-0351928-7

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.
References
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Bibliographic Information
  • © Copyright 1974 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 45 (1974), 295-299
  • MSC: Primary 06A10
  • DOI: https://doi.org/10.1090/S0002-9939-1974-0351928-7
  • MathSciNet review: 0351928