Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.11717 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913203149078528 |
|---|---|
| author | Wang, Zhiyuan Zhou, Jian |
| author_facet | Wang, Zhiyuan Zhou, Jian |
| contents | Using the stratifications of Deligne-Mumford moduli spaces $\overline{\mathcal M}_{g,n}$ indexed by stable graphs, we introduce a partially ordered set of stable graphs by defining a partial ordering on the set of connected stable graphs of genus $g$ with $n$ external edges. By modifying the usual definition of zeta function and Möbius function of a poset, we introduce generalized ($\mathbb Q$-valued) zeta function and generalized ($\mathbb Q$-valued) Möbius function of the poset of stable graphs. We use them to proved a generalized Möbius inversion formula for functions on the poset of stable graphs. Two applications related to duality in earlier work are also presented. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_11717 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Möbius Inversion and Duality for Summations of Stable Graphs Wang, Zhiyuan Zhou, Jian Combinatorics Mathematical Physics Algebraic Geometry Using the stratifications of Deligne-Mumford moduli spaces $\overline{\mathcal M}_{g,n}$ indexed by stable graphs, we introduce a partially ordered set of stable graphs by defining a partial ordering on the set of connected stable graphs of genus $g$ with $n$ external edges. By modifying the usual definition of zeta function and Möbius function of a poset, we introduce generalized ($\mathbb Q$-valued) zeta function and generalized ($\mathbb Q$-valued) Möbius function of the poset of stable graphs. We use them to proved a generalized Möbius inversion formula for functions on the poset of stable graphs. Two applications related to duality in earlier work are also presented. |
| title | Möbius Inversion and Duality for Summations of Stable Graphs |
| topic | Combinatorics Mathematical Physics Algebraic Geometry |
| url | https://arxiv.org/abs/2401.11717 |