Enumeration of posets generated by disjoint unions and ordinal sums-Reference-Cited by-同舟云学术

Enumeration of posets generated by disjoint unions and ordinal sums

Published:1974 Issue:2 Volume:45 Page:295-299
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Stanley Richard P.

Abstract

Let f n {f_n} be the number of n 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 Σ f n x n \Sigma {f_n}{x^n} . Using a result of Bender, an asymptotic estimate can sometimes be given for f n {f_n} . The analogous problem for labeled posets is also considered.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1974-045-02/S0002-9939-1974-0351928-7/S0002-9939-1974-0351928-7.pdf

Reference4 articles.

1. Asymptotic methods in enumeration;Bender, Edward A.;SIAM Rev.,1974

2. The number of finite topologies;Kleitman, D.;Proc. Amer. Math. Soc.,1970

3. Wiley Publications in Mathematical Statistics;Riordan, John,1958

4. J. Wright, Cycle indices of certain classes of quasiorder types or topologies, Dissertation, University of Rochester, Rochester, N. Y., 1972.

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