alexa Simplex and Polygon Equations


Journal of Generalized Lie Theory and Applications

Author(s): Aristophanes Dimakis, Folkert MllerHoissen

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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.
This article was published in SIGMA and referenced in Journal of Generalized Lie Theory and Applications

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