Symmetric Enhancements of Involutory Virtual Birack Counting Invariants

TL;DR

This paper introduces symmetric involutory virtual biracks and shows how good involutions can enhance the counting invariant, providing examples that demonstrate increased strength over the unenhanced invariant.

Contribution

The paper defines symmetric involutory virtual biracks and develops an enhancement of the counting invariant using good involutions, showing it is stronger than the original invariant.

Findings

Enhanced invariant is stronger than the unenhanced counting invariant.

Examples demonstrate the effectiveness of the enhancement.

Good involutions lead to new invariants in virtual knot theory.

Abstract

We consider involutory virtual biracks with good involutions, also known as symmetric involutory virtual biracks. Any good involution on an involutory virtual birack defines an enhancement of the counting invariant. We provide examples demonstrating that the enhancement is stronger than the unenhanced counting invariant.