Cluster Expansions: T-walks, Labeled Posets and Matrix Calculations
We give two new combinatorial methods for computing cluster expansion formulas for arcs coming from possibly punctured surfaces. The first is by using $T$-walks, an extension of the $T$-path model for unpunctured surfaces to general surfaces. We also introduce a new way of generating $T$-paths. The...
Saved in:
| Main Authors | , |
|---|---|
| Format | Journal Article |
| Language | English |
| Published |
15.11.2022
|
| Subjects | |
| Online Access | Get full text |
Cover
Loading…
| Abstract | We give two new combinatorial methods for computing cluster expansion
formulas for arcs coming from possibly punctured surfaces. The first is by
using $T$-walks, an extension of the $T$-path model for unpunctured surfaces to
general surfaces. We also introduce a new way of generating $T$-paths. The
second method is by using order ideals of labeled posets associated to arcs. We
also use the theory of oriented posets to give a quick way to calculate the
expressions using $2$ by $2$ matrices. The techniques introduced are applicable
to different settings in cluster algebras and beyond. |
|---|---|
| AbstractList | We give two new combinatorial methods for computing cluster expansion
formulas for arcs coming from possibly punctured surfaces. The first is by
using $T$-walks, an extension of the $T$-path model for unpunctured surfaces to
general surfaces. We also introduce a new way of generating $T$-paths. The
second method is by using order ideals of labeled posets associated to arcs. We
also use the theory of oriented posets to give a quick way to calculate the
expressions using $2$ by $2$ matrices. The techniques introduced are applicable
to different settings in cluster algebras and beyond. |
| Author | Oğuz, Ezgi Kantarcı Yıldırım, Emine |
| Author_xml | – sequence: 1 givenname: Ezgi Kantarcı surname: Oğuz fullname: Oğuz, Ezgi Kantarcı – sequence: 2 givenname: Emine surname: Yıldırım fullname: Yıldırım, Emine |
| BackLink | https://doi.org/10.48550/arXiv.2211.08011$$DView paper in arXiv |
| BookMark | eNrjYmDJy89LZWCQNDTQM7EwNTXQTyyqyCzTMzIyNNQzsDAwNORkcHbOKS0uSS1ScK0oSMwrzszPK7ZSCNEtT8zJLtZR8ElMSs1JTVEIyC9OLSlWSMxLUfBNLCnKrFBwTsxJLs1JLAFp4GFgTUvMKU7lhdLcDPJuriHOHrpg6-ILijJzE4sq40HWxoOtNSasAgC2lDkJ |
| ContentType | Journal Article |
| Copyright | http://creativecommons.org/licenses/by/4.0 |
| Copyright_xml | – notice: http://creativecommons.org/licenses/by/4.0 |
| DBID | AKZ GOX |
| DOI | 10.48550/arxiv.2211.08011 |
| DatabaseName | arXiv Mathematics arXiv.org |
| DatabaseTitleList | |
| Database_xml | – sequence: 1 dbid: GOX name: arXiv.org url: http://arxiv.org/find sourceTypes: Open Access Repository |
| DeliveryMethod | fulltext_linktorsrc |
| ExternalDocumentID | 2211_08011 |
| GroupedDBID | AKZ GOX |
| ID | FETCH-arxiv_primary_2211_080113 |
| IEDL.DBID | GOX |
| IngestDate | Sat Feb 24 12:22:59 EST 2024 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | false |
| IsScholarly | false |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-arxiv_primary_2211_080113 |
| OpenAccessLink | https://arxiv.org/abs/2211.08011 |
| ParticipantIDs | arxiv_primary_2211_08011 |
| PublicationCentury | 2000 |
| PublicationDate | 2022-11-15 |
| PublicationDateYYYYMMDD | 2022-11-15 |
| PublicationDate_xml | – month: 11 year: 2022 text: 2022-11-15 day: 15 |
| PublicationDecade | 2020 |
| PublicationYear | 2022 |
| Score | 3.7247021 |
| SecondaryResourceType | preprint |
| Snippet | We give two new combinatorial methods for computing cluster expansion
formulas for arcs coming from possibly punctured surfaces. The first is by
using... |
| SourceID | arxiv |
| SourceType | Open Access Repository |
| SubjectTerms | Mathematics - Combinatorics |
| Title | Cluster Expansions: T-walks, Labeled Posets and Matrix Calculations |
| URI | https://arxiv.org/abs/2211.08011 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwdV1NSwMxEB1qT15EUalaNQePBtd8bFdvsrQWseqhwt6WSRpBXFSare7PN5Nd0UuvSUiGhOTNJG9eAM7SLHEh7Ei4lVZylS6QX2VouUMZ8A71CCMZc_aQTp_VXaGLHrDfXBhcNq9frT6w8RdCRIXNhJJ3N4QgytbtY9E-TkYprq79X7vgY8aifyAx2YatzrtjN-1y7EDPve9CnlcrkiNg4yZsPbqd8tdszr-xevPn7B5NOPkX7OnDu9qzENizGcnmNyzHynafa_k9OJ2M5_mUx2HLz1YjoiSLymiR3Id-iOTdABiOtDI2DaBB6aOojVIkb24zvHxBK7MDGKzr5XB91RFsCuLkEzdND6FfL1fuOCBlbU7idP0AEEdsOQ |
| link.rule.ids | 228,230,783,888 |
| linkProvider | Cornell University |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Cluster+Expansions%3A+T-walks%2C+Labeled+Posets+and+Matrix+Calculations&rft.au=O%C4%9Fuz%2C+Ezgi+Kantarc%C4%B1&rft.au=Y%C4%B1ld%C4%B1r%C4%B1m%2C+Emine&rft.date=2022-11-15&rft_id=info:doi/10.48550%2Farxiv.2211.08011&rft.externalDocID=2211_08011 |