Path homology of circulant digraphs
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866908811626807296 |
|---|---|
| author | Tang, Xinxing Yau, Shing-Tung |
| author_facet | Tang, Xinxing Yau, Shing-Tung |
| contents | We organize and extend a set of computations and structural observations about the Grigoryan--Lin--Muranov--Yau (GLMY) path complex of circulant digraphs $\vec{C}_n^S$ and circulant graphs $C_n^S$. Using the shift automorphism $τ$ and a Fourier decomposition, we reduce many rank computations for the GLMY boundary maps to finite-dimensional $τ$-eigenspaces. This provides a reusable "symbol-matrix" recipe that highlights (i) the dependence on prime versus composite $n$ and (ii) stability phenomena for certain natural choices of connection sets $S$. Several fully worked examples are included, together with a discussion of how the additive structure of $S$ governs low-dimensional chains and Betti numbers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_04140 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Path homology of circulant digraphs Tang, Xinxing Yau, Shing-Tung Combinatorics Algebraic Topology We organize and extend a set of computations and structural observations about the Grigoryan--Lin--Muranov--Yau (GLMY) path complex of circulant digraphs $\vec{C}_n^S$ and circulant graphs $C_n^S$. Using the shift automorphism $τ$ and a Fourier decomposition, we reduce many rank computations for the GLMY boundary maps to finite-dimensional $τ$-eigenspaces. This provides a reusable "symbol-matrix" recipe that highlights (i) the dependence on prime versus composite $n$ and (ii) stability phenomena for certain natural choices of connection sets $S$. Several fully worked examples are included, together with a discussion of how the additive structure of $S$ governs low-dimensional chains and Betti numbers. |
| title | Path homology of circulant digraphs |
| topic | Combinatorics Algebraic Topology |
| url | https://arxiv.org/abs/2602.04140 |