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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.
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참고문헌 (10)
참고문헌 신청
B. Sagan / 2001 / The Symmetric Group: Representations, Combinatorial Algorithms, and Symmetric Functions, 2nd edition / Springer-Verlag
H. Whitney / 1932 / A logical expansion in mathematics / Bull. Amer. Math. Soc 38 : 572 ~ 579
I. G. Macdonald / 1995 / Symmetric functions and Hall polynomials,2nd edition / Oxford University Press
O. Egecioglu / 1990 / A combinatorial interpretation of the inverse Kostka matrix / Linear and Multilinear Algebra 26 : 59 ~ 84
R. P. Stanley / 1993 / On immanants of Jacobi-Trudi matrices and permutations with restricted position / J. Combin. Theory Ser. A 62 : 261 ~ 279
H. Whitney / 1932 / A logical expansion in mathematics / Bull. Amer. Math. Soc 38 : 572 ~ 579
I. G. Macdonald / 1995 / Symmetric functions and Hall polynomials,2nd edition / Oxford University Press
O. Egecioglu / 1990 / A combinatorial interpretation of the inverse Kostka matrix / Linear and Multilinear Algebra 26 : 59 ~ 84
R. P. Stanley / 1993 / On immanants of Jacobi-Trudi matrices and permutations with restricted position / J. Combin. Theory Ser. A 62 : 261 ~ 279
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