arXiv subjects

Amy Herron

Publications and source records attributed to Amy Herron.

3 recordsLinked to original sources

arXiv2026

Visualizing conjugation in affine Coxeter groups

Affine Coxeter groups are fundamental objects in mathematics and in crystallography. If two group elements are conjugate, then they have very similar algebraic and geometric properties. Using recent structural results of Mili\'cevi\'c, Schwer and the second author, we develop an app to visualize conjugation in affine Coxeter groups in dimensions 2 and 3. We explain the mathematics underlying this visualization, and connect its visual features to the arts.

math.GR↗

arXiv2025

The Deligne Complex for the $B_3$ Artin Group

We show that the piecewise Euclidean Moussong metric on the Deligne complex of the Artin group of type $B_3$ is $\mathrm{CAT}(0)$. We do this by establishing a criteria for a complex made of $B_3$ simplices to be $\mathrm{CAT}(1)$ in terms of embedded edge paths, which in particular applies to the spherical Deligne complex of type $B_3$. This provides one more step to showing that the Moussong metric is $\mathrm{CAT}(0)$ for any 3-dimensional Artin group.

math.GR↗

arXiv2025

Triangle Presentations Encoded by Perfect Difference Sets

When James Singer exhibited projective planes for all prime power orders in 1938, he realized these using the trace function of cubic extensions of a finite field and linked trace=0 to perfect difference sets. In 1993, Cartwright, Mantero, Steger, and Zappa found that this trace function can be used to create a triangle presentation, which determines the structure of an ~A_2 building. We demonstrate a new, intrinsic connection between the perfect different sets of Singer and the triangle presentations of Cartwright et al., and show that this connection improves the efficiency of algorithms that generate these triangle presentations. Moreover, we translate the panel-regular groups of Essert (2013) and Witzel (2017) using triangle presentation nomenclature. This translation creates a uniform understanding of the panel-regular groups and vertex-regular groups via triangle presentations.

math.GR↗