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A322012 Number of s-positive simple labeled graphs with n vertices. 1
1, 2, 8, 60, 1009 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A stable partition of a graph is a set partition of the vertices where no edge has both ends in the same block. The chromatic symmetric function is given by X_G = Sum_p m(t(p)) where the sum is over all stable partitions of G, t(p) is the integer partition whose parts are the block-sizes of p, and m is the augmented monomial symmetric function basis (see A321895). A graph is s-positive if, in the expansion of its chromatic symmetric function in terms of Schur functions, all coefficients are nonnegative.

LINKS

Table of n, a(n) for n=1..5.

Richard P. Stanley, A symmetric function generalization of the chromatic polynomial of a graph, Advances in Math. 111 (1995), 166-194.

Richard P. Stanley, Graph colorings and related symmetric functions: ideas and applications, Discrete Mathematics 193 (1998), 267-286.

Richard P. Stanley and John R. Stembridge, On immanants of Jacobi-Trudi matrices and permutations with restricted position, Journal of Combinatorial Theory Series A 62-2 (1993), 261-279.

CROSSREFS

a(n) >= A321979(n).

Cf. A000569, A006125, A229048, A240936, A277203, A321895, A321924, A321925, A321931, A321994.

Sequence in context: A191553 A321979 A139017 * A188324 A208356 A188489

Adjacent sequences:  A322009 A322010 A322011 * A322013 A322014 A322015

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Nov 24 2018

STATUS

approved

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Last modified October 23 11:52 EDT 2021. Contains 348212 sequences. (Running on oeis4.)