On Calculating the Chromatic Symmetric Function
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916626709872640 |
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| author | Mobaraki, Nima Amoei Gerivani, Yasaman Nezhad, Sina Ghasemi |
| author_facet | Mobaraki, Nima Amoei Gerivani, Yasaman Nezhad, Sina Ghasemi |
| contents | This paper investigates methods for calculating the chromatic symmetric function (CSF) of a graph in chromatic-bases and the $m_λ$-basis. Our key contributions include a novel approach for calculating the CSF in chromatic-bases constructed from forests and an efficient method for determining the CSF in the $m_λ$-basis. As applications, we present combinatorial proofs for two known theorems that were originally established using algebraic techniques. Additionally, we demonstrate that an algorithm introduced by Aliste-Prieto, de Mier, Orellana, and Zamora can be viewed as a case of our proposed method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_13411 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Calculating the Chromatic Symmetric Function Mobaraki, Nima Amoei Gerivani, Yasaman Nezhad, Sina Ghasemi Combinatorics 05E05 G.2.1; G.2.2 This paper investigates methods for calculating the chromatic symmetric function (CSF) of a graph in chromatic-bases and the $m_λ$-basis. Our key contributions include a novel approach for calculating the CSF in chromatic-bases constructed from forests and an efficient method for determining the CSF in the $m_λ$-basis. As applications, we present combinatorial proofs for two known theorems that were originally established using algebraic techniques. Additionally, we demonstrate that an algorithm introduced by Aliste-Prieto, de Mier, Orellana, and Zamora can be viewed as a case of our proposed method. |
| title | On Calculating the Chromatic Symmetric Function |
| topic | Combinatorics 05E05 G.2.1; G.2.2 |
| url | https://arxiv.org/abs/2411.13411 |