The photography method: Solving pentagon equation

Author:

Manturov Vassily Olegovich12,Wan Zheyan3ORCID

Affiliation:

1. Moscow Institute of Physics and Technology, Moscow 141700, Russia

2. Nosov Magnitogorsk State Technical University, Zhilyaev Laboratory of mechanics of gradient nanomaterials, 38 Lenin prospect, Magnitogorsk 455000, Russian Federation

3. Yanqi Lake Beijing Institute of Mathematical Sciences and Applications, Beijing 101408, P. R. China

Abstract

In this paper, we consider two applications of the pentagon equation. The first deals with actions of flips on edges of triangulations labeled by rational functions in some variables. The second can be formulated as a system of linear equations with variables corresponding to triangles of a triangulation. The general method says that if there is some general data (say, edge lengths or areas) associated with states (say, triangulations) and a general data transformation rule (say, how lengths or areas are changed under flips) then after returning to the initial state we recover the initial data.

Funder

Russian Science Foundation

Publisher

World Scientific Pub Co Pte Ltd

Subject

Algebra and Number Theory

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