Abstract
In this paper we show that the number of pairwise nonisomorphic two-dimensional posets with n elements is asymptotically equivalent to 1/2n!. This estimate is based on a characterization, in terms of structural decomposition, of two-dimensional posets having a unique representation as the intersection of two linear extensions.
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References
K. A. Baker, P. C. Fishburn, and F. S. Roberts (1971) Partial orders of dimension 2, Networks 2, 11–28.
B. Dushnik and E. Miller (1941) Partially ordered sets, Amer. J. Math. 63, 600–610.
D. J. Kleitman and B. L. Rothschild (1975) Asymptotic enumeration of partial orders on a finite set, Trans. Amer. Math. Soc. 205, 205–220.
R. H. Möhring and F. J. Radermacher (1984) Substitution decomposition for discrete structures and connections with combinatorial optimization, in Algebraic and Combinatorial Methods in Operations Research, pp. 257–355, North-Holland Math. Stud. 95, North-Holland, Amsterdam, New York.
J. Spinard (1982) Two dimensional partial orders, PhD thesis, Princeton University.
R. P. Stanley (1974) Enumeration of posets generated by disjoint unions and ordinal sums, Proc. Amer. Math. Soc. 45, 295–299.
M. Yanakakis (1982) The complexity of the partial order dimension problem, SIAM J. Alg. Disc. Meth. 3, 351–358.
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Communicated by I. Rival
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El-Zahar, M., Sauer, N.W. Asymptotic enumeration of two-dimensional posets. Order 5, 239–244 (1988). https://doi.org/10.1007/BF00354891
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DOI: https://doi.org/10.1007/BF00354891