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A001833
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Number of labeled graded partially ordered sets with n elements.
(Formerly M3067 N1243)
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4
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OFFSET
| 0,3
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COMMENTS
| Here "graded" means that there exists a rank function rk from the poset to the integers such that whenever v covers w in the poset, we have rk(v) = rk(w) + 1. Note that this notion of grading is weaker than in sequence A006860, which counts posets in which all maximal chains have the same length.
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REFERENCES
| D. A. Klarner, The number of graded partially ordered sets, J. Combin. Theory, 6 (1969), 12-19.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| Index entries for sequences related to posets
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EXAMPLE
| The poset on {a, b, c, d, e} defined by the relations a < b < c and d < e is counted by this sequence. (For example, one associated rank function is rk(a) = rk(d) = 0, rk(b) = rk(e) = 1 and rk(c) = 2.) However, the poset defined by the relations a < b < c and a < d < e < c is not graded and so not counted by this sequence.
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CROSSREFS
| Graded posets with no chain of length 3 are counted by A001831.
Sequence in context: A135749 A005647 A158876 * A001035 A166380 A136652
Adjacent sequences: A001830 A001831 A001832 * A001834 A001835 A001836
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KEYWORD
| nonn,more
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Corrected and edited by Joel B. Lewis (jblewis(AT)post.harvard.edu), Mar 28 2011
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