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Simplex and Polygon Equations | | Aristophanes Dimakis
; Folkert Mueller-Hoissen
; | | Date: |
28 Sep 2014 | | 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. | | Source: | arXiv, 1409.7855 | | Services: | Forum | Review | PDF | Favorites | |
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