In 1995, Stanley introduced the chromatic symmetric function of a graph, a symmetric function analog of the classical chromatic polynomial of a graph. The Stanley-Stembridge e-positivity conjecture is a long-standing conjecture that states that the chromatic symmetric function of a certain class of graphs, called incomparability graphs of (3+1)-free posets, has nonnegative coefficients when expanded in the elementary symmetric function basis. In 1996, Gasharov described Schur expansion of the chromatic symmetric function for this class of graphs in terms of P-tableau, a generalization of a standard Young tableau. An open problem is to find a bijective proof of this expansion for all (3+1)-free posets.

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