Computing the determinant of links through Fourier-Hadamard transforms

TL;DR

This paper introduces a new method using Fourier-Hadamard transforms to compute link determinants and explores properties of centrally symmetric links, revealing that such links with an even number of components have zero determinant.

Contribution

The paper presents a novel Fourier-Hadamard transform approach for link determinants and characterizes determinants of centrally symmetric links.

Findings

Determinant of centrally symmetric links with even components is zero.

Fourier-Hadamard transforms can be applied to Boolean functions to compute link determinants.

New insights into the properties of symmetric links and their determinants.

Abstract

In this paper, we present a novel method to compute the determinant of a link using Fourier-Hadamard transforms of Boolean functions. We also investigate the determinant of centrally symmetric links (a special class of strong achiral links). In particular, we show that the determinant of a centrally symmetric link with an even number of components is equals zero.