Simplex and Polygon Equations
It is shown that higher Bruhat orders admit a decomposition into a higher Tamari order, the corresponding dual Tamari order, and a ''mixed order''. We describe simplex equations (including the Yang-Baxter equation) as realizations of higher Bruhat orders. Correspondingly, a famil...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2015 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2015
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/147105 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Simplex and Polygon Equations / A. Dimakis, F. Müller-Hoissen // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 107 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-147105 |
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Dimakis, A. Müller-Hoissen, F. 2019-02-13T16:25:31Z 2019-02-13T16:25:31Z 2015 Simplex and Polygon Equations / A. Dimakis, F. Müller-Hoissen // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 107 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 06A06; 06A07; 52Bxx; 82B23 DOI:10.3842/SIGMA.2015.042 https://nasplib.isofts.kiev.ua/handle/123456789/147105 It is shown that higher Bruhat orders admit a decomposition into a higher Tamari order, the corresponding dual Tamari order, and a ''mixed order''. We describe simplex equations (including the Yang-Baxter equation) as realizations of higher Bruhat orders. Correspondingly, a family of ''polygon equations'' realizes higher Tamari orders. They generalize the well-known pentagon equation. The structure of simplex and polygon equations is visualized in terms of deformations of maximal chains in posets forming 1-skeletons of polyhedra. The decomposition of higher Bruhat orders induces a reduction of the N-simplex equation to the (N+1)-gon equation, its dual, and a compatibility equation. We have to thank an anonymous referee for comments that led to some corrections in our previous version of Section 2.2. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Simplex and Polygon Equations Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Simplex and Polygon Equations |
| spellingShingle |
Simplex and Polygon Equations Dimakis, A. Müller-Hoissen, F. |
| title_short |
Simplex and Polygon Equations |
| title_full |
Simplex and Polygon Equations |
| title_fullStr |
Simplex and Polygon Equations |
| title_full_unstemmed |
Simplex and Polygon Equations |
| title_sort |
simplex and polygon equations |
| author |
Dimakis, A. Müller-Hoissen, F. |
| author_facet |
Dimakis, A. Müller-Hoissen, F. |
| publishDate |
2015 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
It is shown that higher Bruhat orders admit a decomposition into a higher Tamari order, the corresponding dual Tamari order, and a ''mixed order''. We describe simplex equations (including the Yang-Baxter equation) as realizations of higher Bruhat orders. Correspondingly, a family of ''polygon equations'' realizes higher Tamari orders. They generalize the well-known pentagon equation. The structure of simplex and polygon equations is visualized in terms of deformations of maximal chains in posets forming 1-skeletons of polyhedra. The decomposition of higher Bruhat orders induces a reduction of the N-simplex equation to the (N+1)-gon equation, its dual, and a compatibility equation.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/147105 |
| citation_txt |
Simplex and Polygon Equations / A. Dimakis, F. Müller-Hoissen // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 107 назв. — англ. |
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AT dimakisa simplexandpolygonequations AT mullerhoissenf simplexandpolygonequations |
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2025-11-27T20:19:10Z |
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2025-11-27T20:19:10Z |
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1850852756133249024 |