Sato tau functions and construction of Somos sequence

TL;DR

This paper reconstructs the KP equation from Plucker relations, introduces a discrete tau function, and constructs new integer sequences, including one not listed in OEIS, demonstrating novel sequence generation methods.

Contribution

It presents a novel approach to constructing integer sequences via tau functions derived from KP equations and Plucker relations, expanding the catalog of known sequences.

Findings

Constructed a new integer sequence not in OEIS.

Generalized the KP equation through Plucker relations.

Developed a method to generate many new sequences.

Abstract

In this short article, we will reconstruct the KP equation from Plucker relations and provide some generalizations on this topic. Additionally, in the final section, we define the discrete function $\tau$ in a similar manner, leading to the construction of an integer sequence that has not yet been listed in the OEIS. Furthermore, this approach allows us to construct many other sequences that are not listed in the OEIS.