

A322012


Number of spositive simple labeled graphs with n vertices.


1




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 blocksizes of p, and m is the augmented monomial symmetric function basis (see A321895). A graph is spositive 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), 166194.
Richard P. Stanley, Graph colorings and related symmetric functions: ideas and applications, Discrete Mathematics 193 (1998), 267286.
Richard P. Stanley and John R. Stembridge, On immanants of JacobiTrudi matrices and permutations with restricted position, Journal of Combinatorial Theory Series A 622 (1993), 261279.


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



