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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 (seeA321895). A graph is s-positive if, in the expansion of its chromatic symmetric function in terms of Schur functions, all coefficients are nonnegative.

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.

a(n) >=A321979(n).

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

Sequence in context:A191553A321979A139017 *A188324A368450A370913

Adjacent sequences:A322009A322010A322011 *A322013A322014A322015

nonn,more

Gus Wiseman, Nov 24 2018

approved