OFFSET
0,3
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.
REFERENCES
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).
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..100
David A. Klarner, The number of graded partially ordered sets, Journal of Combinatorial Theory, vol.6, no.1, pp.12-19, (January-1969).
D. A. Klarner, The number of graded partially ordered sets, J. Combin. Theory, 6 (1969), 12-19. [Annotated scanned copy]
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.
PROG
(PARI) \\ C(n) is defined in A361951.
seq(n)={my(c=C(n)); Vec(serlaplace(c[n+1]/c[n]))} \\ Andrew Howroyd, Mar 31 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
Corrected and edited by Joel B. Lewis, Mar 28 2011
a(7)-a(15) from Daniele P. Morelli, Aug 25 2013
a(16)-a(18) from Sean A. Irvine, Sep 25 2015
STATUS
approved