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%I #5 Nov 24 2018 08:15:48
%S 1,2,8,60,1009
%N Number of s-positive simple labeled graphs with n vertices.
%C 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.
%H Richard P. Stanley, <a href="http://www-math.mit.edu/~rstan/pubs/pubfiles/100.pdf">A symmetric function generalization of the chromatic polynomial of a graph</a>, Advances in Math. 111 (1995), 166-194.
%H Richard P. Stanley, <a href="http://www-math.mit.edu/~rstan/papers/taor.pdf">Graph colorings and related symmetric functions: ideas and applications</a>, Discrete Mathematics 193 (1998), 267-286.
%H Richard P. Stanley and John R. Stembridge, <a href="https://doi.org/10.1016/0097-3165(93)90048-D">On immanants of Jacobi-Trudi matrices and permutations with restricted position</a>, Journal of Combinatorial Theory Series A 62-2 (1993), 261-279.
%Y a(n) >= A321979(n).
%Y Cf. A000569, A006125, A229048, A240936, A277203, A321895, A321924, A321925, A321931, A321994.
%K nonn,more
%O 1,2
%A _Gus Wiseman_, Nov 24 2018
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