Enumerative combinatorics
On the cover polynomial of a digraph
Journal of Combinatorial Theory Series B
Incomparability graphs of (3 + 1)-free posets are s-positive
Proceedings of the 6th conference on Formal power series and algebraic combinatorics
A Robinson-Schensted algorithm for a class of partial orders
Journal of Combinatorial Theory Series A
Discrete Mathematics - selected papers in honor of Adriano Garsia
The Coloring Ideal and Coloring Complex of a Graph
Journal of Algebraic Combinatorics: An International Journal
Note: properties of the descent algebras of type D
Discrete Mathematics
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We investigate an apparent hodgepodge of topics: a Robinson-Schensted algorithmfor (3 + 1)-free posets, Chung and Graham‘s G-descent expansion of the chromaticpolynomial, a quasi-symmetric expansion of the path-cycle symmetric function,and an expansion of Stanley‘s chromatic symmetric function X_G in termsof a new symmetric function basis. We show how the theory of P-partitions(in particular, Stanley‘s quasi-symmetric function expansion of the chromaticsymmetric function X_G) unifies them all, subsuming two old resultsand implying two new ones. Perhaps our most interesting result relates to thestill-open problem of finding a Robinson-Schensted algorithm for (3 + 1)-free posets.(Magid has announced a solution but it appears to be incorrect.) We show thatsuch an algorithm ought to “respect descents,” and that the best partialalgorithm so far—due to Sundquist, Wagner, and West—respects descents if it avoids a certain induced subposet.