The existence of Hall polynomials for posets of finite prinjective type

TL;DR

This paper proves the existence of Hall polynomials for prinjective representations of finite posets of finite prinjective type, enabling the construction of a generic Ringel-Hall algebra for these representations.

Contribution

It establishes the existence of Hall polynomials in this context, which was previously unknown, and discusses their implications for algebraic structures.

Findings

Hall polynomials exist for prinjective representations of finite posets

A generic Ringel-Hall algebra can be defined for these representations

The results have implications for algebraic and representation theory

Abstract

We prove the existence of Hall polynomials for prinjective representations of finite partially ordered sets of finite prinjective type. In Section 4 we shortly discuss consequences of the existence of Hall polynomials, in particular, we are able to define a generic Ringel-Hall algebra for prinjective representations of posets of finite prinjective type.