On the Topology of the Cambrian Semilattices
For an arbitrary Coxeter group $W$, David Speyer and Nathan Reading defined Cambrian semilattices $C_{\gamma}$ as certain sub-semilattices of the weak order on $W$. In this article, we define an edge-labelling using the realization of Cambrian semilattices in terms of $\gamma$-sortable elements, and...
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2013-01-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
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| Online Access: | https://dmtcs.episciences.org/2320/pdf |
| _version_ | 1797270299605991424 |
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| author | Myrto Kallipoliti Henri Mühle |
| author_facet | Myrto Kallipoliti Henri Mühle |
| author_sort | Myrto Kallipoliti |
| collection | DOAJ |
| description | For an arbitrary Coxeter group $W$, David Speyer and Nathan Reading defined Cambrian semilattices $C_{\gamma}$ as certain sub-semilattices of the weak order on $W$. In this article, we define an edge-labelling using the realization of Cambrian semilattices in terms of $\gamma$-sortable elements, and show that this is an EL-labelling for every closed interval of $C_{\gamma}$. In addition, we use our labelling to show that every finite open interval in a Cambrian semilattice is either contractible or spherical, and we characterize the spherical intervals, generalizing a result by Nathan Reading. |
| first_indexed | 2024-04-25T02:02:04Z |
| format | Article |
| id | doaj.art-aed23a4911c147e09796180e4839842b |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:02:04Z |
| publishDate | 2013-01-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-aed23a4911c147e09796180e4839842b2024-03-07T14:52:36ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502013-01-01DMTCS Proceedings vol. AS,...Proceedings10.46298/dmtcs.23202320On the Topology of the Cambrian SemilatticesMyrto Kallipoliti0https://orcid.org/0000-0003-2188-6552Henri Mühle1https://orcid.org/0000-0003-1888-7247Fakultät für Mathematik [Wien]Fakultät für Mathematik [Wien]For an arbitrary Coxeter group $W$, David Speyer and Nathan Reading defined Cambrian semilattices $C_{\gamma}$ as certain sub-semilattices of the weak order on $W$. In this article, we define an edge-labelling using the realization of Cambrian semilattices in terms of $\gamma$-sortable elements, and show that this is an EL-labelling for every closed interval of $C_{\gamma}$. In addition, we use our labelling to show that every finite open interval in a Cambrian semilattice is either contractible or spherical, and we characterize the spherical intervals, generalizing a result by Nathan Reading.https://dmtcs.episciences.org/2320/pdfcoxeter groupsweak ordercambrian semilatticesel-shellability[info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| spellingShingle | Myrto Kallipoliti Henri Mühle On the Topology of the Cambrian Semilattices Discrete Mathematics & Theoretical Computer Science coxeter groups weak order cambrian semilattices el-shellability [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| title | On the Topology of the Cambrian Semilattices |
| title_full | On the Topology of the Cambrian Semilattices |
| title_fullStr | On the Topology of the Cambrian Semilattices |
| title_full_unstemmed | On the Topology of the Cambrian Semilattices |
| title_short | On the Topology of the Cambrian Semilattices |
| title_sort | on the topology of the cambrian semilattices |
| topic | coxeter groups weak order cambrian semilattices el-shellability [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| url | https://dmtcs.episciences.org/2320/pdf |
| work_keys_str_mv | AT myrtokallipoliti onthetopologyofthecambriansemilattices AT henrimuhle onthetopologyofthecambriansemilattices |