Spectral Antisymmetry of Twisted Graph Adjacency
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915246586724352 |
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| author | Luo, Ye Roy, Arindam |
| author_facet | Luo, Ye Roy, Arindam |
| contents | We address a prime counting problem across the homology classes of a graph, presenting a graph-theoretical Dirichlet-type analogue of the prime number theorem. The main machinery we have developed and employed is a spectral antisymmetry theorem, revealing that the spectra of the twisted graph adjacency matrices have an antisymmetric distribution over the character group of the graph with a special character called the canonical character being an extremum. Additionally, we derive some trace formulas based on the twisted adjacency matrices as part of our analysis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_01550 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Spectral Antisymmetry of Twisted Graph Adjacency Luo, Ye Roy, Arindam Combinatorics Discrete Mathematics Number Theory Spectral Theory 05C50, 05C38, 11M41 We address a prime counting problem across the homology classes of a graph, presenting a graph-theoretical Dirichlet-type analogue of the prime number theorem. The main machinery we have developed and employed is a spectral antisymmetry theorem, revealing that the spectra of the twisted graph adjacency matrices have an antisymmetric distribution over the character group of the graph with a special character called the canonical character being an extremum. Additionally, we derive some trace formulas based on the twisted adjacency matrices as part of our analysis. |
| title | Spectral Antisymmetry of Twisted Graph Adjacency |
| topic | Combinatorics Discrete Mathematics Number Theory Spectral Theory 05C50, 05C38, 11M41 |
| url | https://arxiv.org/abs/2403.01550 |