The column group and its link invariants

TL;DR

This paper introduces a new enhancement of the integral birack counting invariant using subgroups of the column group linked to birack homomorphisms, demonstrating it can distinguish more cases than previous invariants.

Contribution

It defines a novel invariant enhancement based on column group subgroups and demonstrates its increased discriminative power over existing invariants.

Findings

Enhanced invariant distinguishes more biracks than the unenhanced version

Uses subgroups of the column group linked to birack homomorphisms

Provides examples illustrating the improved discrimination

Abstract

The column group is a subgroup of the symmetric group on the elements of a finite blackboard birack generated by the column permutations in the birack matrix. We use subgroups of the column group associated to birack homomorphisms to define an enhancement of the integral birack counting invariant and give examples which show that the enhanced invariant is stronger than the unenhanced invariant.