Grouped Stirling complexes
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866912894556307456 |
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| author | Revelli, Alessia Scheirer, Steven |
| author_facet | Revelli, Alessia Scheirer, Steven |
| contents | Given a graph $G$, a configuration space of $G$ can be thought of as the set of all possible configurations of "robots" which can move throughout $G$, subject to some constraints. We introduce a type of configuration space which we call Grouped Stirling complexes, denoted by $S_{\vec r}(G)$, in which we place robots in groups subject to two constraints. First, there must be at least one robot on each vertex of $G$, and second, any two robots from the same group must be "separated by at least one full open edge" of $G$. The space $S_{\vec r}(G)$ has a closed cell structure, which means it can be built out of cells of various dimensions. Our main results show $S_{\vec r}(G)$ is path-connected, provided there are at least three groups, and determine the number of cells of $S_{\vec r}(G)$ in certain cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_09884 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Grouped Stirling complexes Revelli, Alessia Scheirer, Steven Combinatorics 57-02 (Primary), 05A15 (Secondary) Given a graph $G$, a configuration space of $G$ can be thought of as the set of all possible configurations of "robots" which can move throughout $G$, subject to some constraints. We introduce a type of configuration space which we call Grouped Stirling complexes, denoted by $S_{\vec r}(G)$, in which we place robots in groups subject to two constraints. First, there must be at least one robot on each vertex of $G$, and second, any two robots from the same group must be "separated by at least one full open edge" of $G$. The space $S_{\vec r}(G)$ has a closed cell structure, which means it can be built out of cells of various dimensions. Our main results show $S_{\vec r}(G)$ is path-connected, provided there are at least three groups, and determine the number of cells of $S_{\vec r}(G)$ in certain cases. |
| title | Grouped Stirling complexes |
| topic | Combinatorics 57-02 (Primary), 05A15 (Secondary) |
| url | https://arxiv.org/abs/2602.09884 |