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arXiv · 2609.22708

Chromatic symmetric functions for annular webs

Jaeseong Oh·Seokbeom Yoon
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Abstract

We introduce a combinatorial definition of chromatic symmetric functions for annular webs. We prove their symmetry by constructing a web analogue of the Shareshian--Wachs involution and show that they coincide with the symmetric functions associated to annular webs via Turaev's isomorphism. We then derive explicit formulas for their hook Schur coefficients. We also introduce web LLT functions, whose hook Schur coefficients admit positive Laurent-polynomial formulas. These formulas yield a combinatorial expression for the coefficients of the HOMFLY--PT polynomial of an annular web.

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Jaeseong Oh, Seokbeom Yoon. 2026-09-19. Chromatic symmetric functions for annular webs. https://arxiv.org/abs/2609.22708

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