Enumeration of posets generated by disjoint unions and ordinal sums
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- by Richard P. Stanley PDF
- Proc. Amer. Math. Soc. 45 (1974), 295-299 Request permission
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
- Edward A. Bender, Asymptotic methods in enumeration, SIAM Rev. 16 (1974), 485–515. MR 376369, DOI 10.1137/1016082
- D. Kleitman and B. Rothschild, The number of finite topologies, Proc. Amer. Math. Soc. 25 (1970), 276–282. MR 253944, DOI 10.1090/S0002-9939-1970-0253944-9
- John Riordan, An introduction to combinatorial analysis, Wiley Publications in Mathematical Statistics, John Wiley & Sons, Inc., New York; Chapman & Hall, Ltd., London, 1958. MR 0096594 J. Wright, Cycle indices of certain classes of quasiorder types or topologies, Dissertation, University of Rochester, Rochester, N. Y., 1972.
Additional 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