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PreprintCC BY 4.0arXiv

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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Cite

BibTeXRIS
BibTeX
@misc{oh2026chromatic,
  title = {{Chromatic symmetric functions for annular webs}},
  author = {Jaeseong Oh and Seokbeom Yoon},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.22708},
  eprint = {2609.22708},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.22708},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Chromatic symmetric functions for annular webs
AU  - Jaeseong Oh
AU  - Seokbeom Yoon
PY  - 2026
DA  - 2026/09/19
PB  - arXiv
DO  - 10.48550/arxiv.2609.22708
UR  - https://arxiv.org/abs/2609.22708
AB  - 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.
ER  -