Macdonald polynomials and chromatic quasisymmetric functions

Andrew Timothy Wilson; James Haglund

Macdonald polynomials and chromatic quasisymmetric functions

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arxiv 1701.05622 v2 pith:TTKZZEUE submitted 2017-01-19 math.CO

James Haglund , Andrew Timothy Wilson This is my paper · ORCID

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keywords polynomialsformfunctionsintegralmacdonaldchromaticquasisymmetricformulas

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We express the integral form Macdonald polynomials as a weighted sum of Shareshian and Wachs' chromatic quasisymmetric functions of certain graphs. Then we use known expansions of these chromatic quasisymmetric functions into Schur and power sum symmetric functions to provide Schur and power sum formulas for the integral form Macdonald polynomials. Since the (integral form) Jack polynomials are a specialization of integral form Macdonald polynomials, we obtain analogous formulas for Jack polynomials as corollaries.

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Chromatic nonsymmetric polynomials of Dyck graphs are slide-positive
math.CO 2019-08 conditional novelty 6.0 of 10

Chromatic nonsymmetric polynomials of Dyck graphs are slide-positive, and their backstable limit recovers the known fundamental-basis expansion of chromatic quasisymmetric functions.

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