Some incidence theorems and integrable discrete equations

Abstract

Several incidence theorems of planar projective geometry are considered. It is demonstrated that generalizations of Pascal theorem due to Möbius give rise to double cross-ratio equation and Hietarinta equation. The construction corresponding to the double cross-ratio equation is a reduction to a conic section of some planar configuration $(20_{3}15_4)$. This configuration provides a correct definition of the multidimensional quadrilateral lattices on the plane.

12 p, 7 fig

References in corpus (1)

• A new two-dimensional lattice model that is "consistent around a cube"

Cited by in corpus (4)

• Incircular nets and confocal conics
• Discrete integrable systems and deformations of associative algebras
• Quadrangular sets in projective line and in Moebius space, and geometric interpretation of the non-commutative discrete Schwarzian Kadomtsev-Petviashvili equation
• Coble's group and the integrability of the Gosset-Elte polytopes and tessellations