The Rhodes semilattice of a biased graph
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910303922421760 |
|---|---|
| author | Gottstein, Michael J. Zaslavsky, Thomas |
| author_facet | Gottstein, Michael J. Zaslavsky, Thomas |
| contents | We reinterpret the Rhodes semilattices $R_n(\mathfrak{G})$ of a group $\mathfrak{G}$ in terms of gain graphs and generalize them to all gain graphs, both as sets of partition-potential pairs and as sets of subgraphs, and for the latter, further to biased graphs. Based on this we propose four different natural lattices in which the Rhodes semilattices and its generalizations are order ideals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_02700 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The Rhodes semilattice of a biased graph Gottstein, Michael J. Zaslavsky, Thomas Combinatorics 06A12 (Primary) 05B35, 05C22, 06C10, 20L05 (Secondary) We reinterpret the Rhodes semilattices $R_n(\mathfrak{G})$ of a group $\mathfrak{G}$ in terms of gain graphs and generalize them to all gain graphs, both as sets of partition-potential pairs and as sets of subgraphs, and for the latter, further to biased graphs. Based on this we propose four different natural lattices in which the Rhodes semilattices and its generalizations are order ideals. |
| title | The Rhodes semilattice of a biased graph |
| topic | Combinatorics 06A12 (Primary) 05B35, 05C22, 06C10, 20L05 (Secondary) |
| url | https://arxiv.org/abs/2309.02700 |