Rooted Clusters for Graph LP Algebras
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Abstract
- LP algebras, introduced by Lam and Pylyavskyy, are a generalization of cluster algebras. These algebras are known to have the Laurent phenomenon, but positivity remains conjectural. Graph LP algebras are finite LP algebras encoded by a graph. For the graph LP algebra defined by a tree, we define a family of clusters called rooted clusters. We prove positivity for these clusters by giving explicit formulas for each cluster variable. We also give a combinatorial interpretation for these expansions using a generalization of T-paths.
| Title | Rooted Clusters for Graph LP Algebras |
|---|---|
| Creator | Kelley, E. |
| Zhang, S. W. | |
| Chepuri, Sunita | |
| Banaian, E. | |
| Publisher | SIGMA |
| Academic Department | Mathematics |
| Division | Natural Sciences |
| Organization | Lafayette College |
| Date Issued | 2022 |
| Date Available | 2022-12-15 |
| Type | Article |
| Language | English |
| Keyword | T-path |
| Laurent phenomenon algebra | |
| graph LP algebra | |
| cluster algebra | |
| Bibliographic Citation | Banaian, E., et al. (2022) "Rooted Clusters for Graph LP Algebras." SIGMA 18: 089. |
| Standard Identifier | Handle 10385/n583xw72h |
| DOI 10.3842/SIGMA.2022.089 | |
| Permalink | http://hdl.handle.net/10385/n583xw72h |
| Rights Statement |
Creative Commons - Attribution, ShareAlike
|
| Rights Holders | Kelley, E. |
| Banaian, E. | |
| Chepuri, Sunita | |
| Zhang, S. W. |
Contains
| File | Chepuri-SIGMA-vol18-2022.pdf | Uploaded 2022-12-15 | Public | Download |
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