A τ-Tilting Approach to Dissections of Polygons
We show that any accordion complex associated to a dissection of a convex polygon is isomorphic to the support τ-tilting simplicial complex of an explicit finite-dimensional algebra. To this end, we prove a property of some induced subcomplexes of support τ-tilting simplicial complexes of finite-dim...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2018 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2018
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/209527 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | A τ-Tilting Approach to Dissections of Polygons / V. Pilaud, P.-G. Plamondon, S. Stella // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 16 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862724692981317632 |
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| author | Pilaud, V. Plamondon, P.-G. Stella, S. |
| author_facet | Pilaud, V. Plamondon, P.-G. Stella, S. |
| citation_txt | A τ-Tilting Approach to Dissections of Polygons / V. Pilaud, P.-G. Plamondon, S. Stella // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 16 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We show that any accordion complex associated to a dissection of a convex polygon is isomorphic to the support τ-tilting simplicial complex of an explicit finite-dimensional algebra. To this end, we prove a property of some induced subcomplexes of support τ-tilting simplicial complexes of finite-dimensional algebras.
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| first_indexed | 2025-12-07T18:48:35Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-209527 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T18:48:35Z |
| publishDate | 2018 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Pilaud, V. Plamondon, P.-G. Stella, S. 2025-11-24T10:41:22Z 2018 A τ-Tilting Approach to Dissections of Polygons / V. Pilaud, P.-G. Plamondon, S. Stella // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 16 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 16G10; 16G20; 05E10 arXiv: 1710.02119 https://nasplib.isofts.kiev.ua/handle/123456789/209527 https://doi.org/10.3842/SIGMA.2018.045 We show that any accordion complex associated to a dissection of a convex polygon is isomorphic to the support τ-tilting simplicial complex of an explicit finite-dimensional algebra. To this end, we prove a property of some induced subcomplexes of support τ-tilting simplicial complexes of finite-dimensional algebras. We are grateful to F. Chapoton for pointing out to us the isomorphism between the two graphs of Fig. 2, which gave us the motivation for the present note. We also thank R. Schiffler for his comments on a previous version. Finally, we are grateful to an anonymous referee for helpful suggestions on the presentation of this note. The first two authors are partially supported by the French ANR grant SC3A (15 CE40 0004 01). The last author is supported by the ISF grant 1144/16. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications A τ-Tilting Approach to Dissections of Polygons Article published earlier |
| spellingShingle | A τ-Tilting Approach to Dissections of Polygons Pilaud, V. Plamondon, P.-G. Stella, S. |
| title | A τ-Tilting Approach to Dissections of Polygons |
| title_full | A τ-Tilting Approach to Dissections of Polygons |
| title_fullStr | A τ-Tilting Approach to Dissections of Polygons |
| title_full_unstemmed | A τ-Tilting Approach to Dissections of Polygons |
| title_short | A τ-Tilting Approach to Dissections of Polygons |
| title_sort | τ-tilting approach to dissections of polygons |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/209527 |
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