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A deletion–contraction long exact sequence for chromatic symmetric homology.
- Source :
-
European Journal of Combinatorics . Jan2024, Vol. 115, pN.PAG-N.PAG. 1p. - Publication Year :
- 2024
-
Abstract
- In Crew and Spirkl (2020), the authors generalize Stanley's chromatic symmetric function (Stanley, 1995) to vertex-weighted graphs. In this paper we find a categorification of their new invariant extending the definition of chromatic symmetric homology to vertex-weighted graphs. We prove the existence of a deletion–contraction long exact sequence for chromatic symmetric homology which gives a useful computational tool and allow us to answer two questions left open in Chandler et al. (2019). In particular, we prove that, for a graph G with n vertices, the maximal index with nonzero homology is not greater that n − 1. Moreover, we show that the homology is non-trivial for all the indices between the minimum and the maximum with this property. [ABSTRACT FROM AUTHOR]
- Subjects :
- *SYMMETRIC functions
*HOMOLOGY theory
*OPEN-ended questions
*HOMOLOGY (Biology)
Subjects
Details
- Language :
- English
- ISSN :
- 01956698
- Volume :
- 115
- Database :
- Academic Search Index
- Journal :
- European Journal of Combinatorics
- Publication Type :
- Academic Journal
- Accession number :
- 172846645
- Full Text :
- https://doi.org/10.1016/j.ejc.2023.103788