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This article is cited in 19 scientific papers (total in 19 papers)
Simplex and Polygon Equations
Aristophanes Dimakisa, Folkert Müller-Hoissenb a Department of Financial and Management Engineering, University of the Aegean, 82100 Chios, Greece
b Max Planck Institute for Dynamics and Self-Organization, 37077 Göttingen, Germany
Abstract:
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.
Keywords:
higher Bruhat order; higher Tamari order; pentagon equation; simplex equation.
Received: October 23, 2014; in final form May 26, 2015; Published online June 5, 2015
Citation:
Aristophanes Dimakis, Folkert Müller-Hoissen, “Simplex and Polygon Equations”, SIGMA, 11 (2015), 042, 49 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1023 https://www.mathnet.ru/eng/sigma/v11/p42
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Abstract page: | 356 | Full-text PDF : | 58 | References: | 34 |
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