Properties of HYMNs in Examples of Four-Color, Five-Color, and Six-Color Adinkras

TL;DR

This paper investigates the properties of HYMNs, eigenvalues derived from Banchoff matrices, in various colored adinkras, revealing insights into their shape and structure in discrete Morse theory context.

Contribution

It introduces the analysis of HYMNs in different colored adinkras, connecting Banchoff matrices to the shape characterization of these structures.

Findings

HYMNs are computed for four-color, five-color, and six-color adinkras.

Properties of HYMNs reflect the shape and structure of adinkras.

Eigenvalues of Banchoff matrices reveal structural insights.

Abstract

The mathematical concept of a "Banchoff index" associated with discrete Morse functions for oriented triangular meshes has been shown to correspond to the height assignments of nodes in adinkras. In recent work there has been introduced the concept of "Banchoff matrices" leading to HYMNs - height yielding matrix numbers. HYMNs map the shape of an adinkra to a set of eigenvalues derived from Banchoff matrices. In the context of some examples of four-color, minimal five-color, and minimal six-color adinkras, properties of the HYMNs are explored.