COMBINATORIAL PROOF FOR e-POSITIVITY OF THE POSET OF RANK 1
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Let P be a poset and G = G(P) be the incomparability graph of P. Stanley [7] defined the chromatic symmetric function XG(P) which generalizes the chromatic polynomial G of G, and showed all coefficients are nonnegative in the e-expansion of XG(P) for a poset P of rank 1. In this paper, we construct a sign reversing involution on the set of special rim hook P-tableaux with some conditions. It gives a combinatorial proof for (3+1)-free conjecture of a poset P of rank 1.
Abstract
Let P be a poset and G = G(P) be the incomparability graph of P. Stanley [7] defined the chromatic symmetric function XG(P) which generalizes the chromatic polynomial G of G, and showed all coefficients are nonnegative in the e-expansion of XG(P) for a poset P of rank 1. In this paper, we construct a sign reversing involution on the set of special rim hook P-tableaux with some conditions. It gives a combinatorial proof for (3+1)-free conjecture of a poset P of rank 1.
참고문헌 (10)
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