Pentagram-Type Maps and the Discrete KP Equation.

We investigate the integrability of a family of pentagram maps proposed by M. Glick and P. Pylyavskyy, which share the property that each generates an infinite configuration of points and lines with four points on each line. Their Lax representations with spectral parameters are constructed. It’s important to emphasize that the proofs we provide are presented at a physical level of rigor, acknowledging that the periodicity aspect requires further meticulous treatment to establish complete mathematical rigor. Moreover, our investigation reveals a connection between these pentagram-type maps and the discrete KP equation. Finally, their continuous limits are considered. [ABSTRACT FROM AUTHOR]