Perpetuants: A Lost Treasure

TL;DR

This paper revisits the classical concept of perpetuants, providing a proof of their dimension theorem and presenting a basis, thereby completing a long-standing mathematical investigation.

Contribution

It offers a rigorous proof of the dimension theorem for perpetuants and constructs an explicit basis, reviving a historical mathematical concept.

Findings

Proof of the Theorem of Stroh for perpetuants

Explicit basis of perpetuants constructed

Closure of a long-standing mathematical investigation

Abstract

We discuss the classical, and forgotten, notion of perpetuants. We give a proof of the Theorem of Stroh computing their dimensions, and exhibit a basis of perpetuants, thus closing an old line of investigation.