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 | References | Similar Articles | Additional Information

Abstract: Let be the number of -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 . Using a result of Bender, an asymptotic estimate can sometimes be given for . The analogous problem for labeled posets is also considered.

**[1]**Edward A. Bender,*Asymptotic methods in enumeration*, SIAM Rev.**16**(1974), 485–515. MR**0376369****[2]**D. Kleitman and B. Rothschild,*The number of finite topologies*, Proc. Amer. Math. Soc.**25**(1970), 276–282. MR**0253944**, 10.1090/S0002-9939-1970-0253944-9**[3]**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****[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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DOI:
https://doi.org/10.1090/S0002-9939-1974-0351928-7

Keywords:
Poset,
partially ordered set,
disjoint union,
ordinal sum,
generating function,
Pólya's enumeration theorem,
functional equation

Article copyright:
© Copyright 1974
American Mathematical Society