Indecomposable invariants of quivers for dimension (2,...,2) and maximal paths, II

TL;DR

This paper establishes an upper bound on the degrees of minimal generating invariants for quivers of dimension (2,...,2), providing precise estimates and reducing the problem to describing certain maximal paths.

Contribution

It introduces a new upper bound for invariants of quivers in dimension (2,...,2) and reduces the problem to analyzing maximal paths with specific properties.

Findings

Upper bound on degrees of invariants is established.

The bound is valid over fields of arbitrary characteristic.

The problem is reduced to describing maximal paths with certain conditions.

Abstract

An upper bound on degrees of elements of a minimal generating system for invariants of quivers of dimension (2,...,2) is established over a field of arbitrary characteristic and its precision is estimated. The proof is based on the reduction to the problem of description of maximal paths satisfying certain condition.