Determining the group that sends each Legendre pair to an equivalent Legendre pair

TL;DR

This paper characterizes the group of transformations that map Legendre pairs to equivalent pairs, providing insight into their structural properties.

Contribution

It identifies the complete structure of the group of operations preserving Legendre pair equivalence.

Findings

The group of all such operations is explicitly determined.

The structure of this group reveals symmetries of Legendre pairs.

This work advances understanding of Legendre pair equivalence classes.

Abstract

In this paper we determine the structure of the group of all operations that send each Legendre pair to an equivalent Legendre pair.