Chromatic quasisymmetric functions of the path graph
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912251375517696 |
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| author | Aliniaeifard, Farid Asgarli, Shamil Esipova, Maria Shelburne, Ethan van Willigenburg, Stephanie Whitehead, Tamsen |
| author_facet | Aliniaeifard, Farid Asgarli, Shamil Esipova, Maria Shelburne, Ethan van Willigenburg, Stephanie Whitehead, Tamsen |
| contents | We show that the chromatic quasisymmetric function (CQF) of a labeled path graph on $n$ vertices is not symmetric unless the labeling is the natural labeling $1, 2, ..., n$ or its reverse $n, ..., 2, 1$. We also show that the star graph $K_{1, n-1}$ with $n\geq 3$ has a nonsymmetric CQF for all labelings. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_14455 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Chromatic quasisymmetric functions of the path graph Aliniaeifard, Farid Asgarli, Shamil Esipova, Maria Shelburne, Ethan van Willigenburg, Stephanie Whitehead, Tamsen Combinatorics Primary: 05C05, 05E05, Secondary: 05C20, 05C25, 16T30 We show that the chromatic quasisymmetric function (CQF) of a labeled path graph on $n$ vertices is not symmetric unless the labeling is the natural labeling $1, 2, ..., n$ or its reverse $n, ..., 2, 1$. We also show that the star graph $K_{1, n-1}$ with $n\geq 3$ has a nonsymmetric CQF for all labelings. |
| title | Chromatic quasisymmetric functions of the path graph |
| topic | Combinatorics Primary: 05C05, 05E05, Secondary: 05C20, 05C25, 16T30 |
| url | https://arxiv.org/abs/2408.14455 |