Descents, quasi-symmetric functions, and the chromatic symmetric function

Details Descents, quasi-symmetric functions, and the chromatic symmetric function Descents, quasi-symmetric functions, and the chromatic symmetric function

1997-12-04

arxiv.org/abs/math/9712229v1

Mathematics

Combinatorics

14 pages

Scientific paper

We give a new proof of Chung and Graham's ``G-descent expansion'' of the classical chromatic polynomial, as well as a special case of the quasi-symmetric function expansion of the path-cycle symmetric function Xi_D. Both proofs rely on Stanley's quasi-symmetric function expansion of the chromatic symmetric function X_G. We also show that Stanley's expansion suggests that a Robinson-Schensted algorithm for (3+1)-free posets---something that has been sought for unsuccessfully for some time---ought to ``respect descents'' in a certain precise sense.

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