The distance signatures of the incidence graphs of affine resolvable designs

TL;DR

This paper determines the distance signatures of incidence matrices in affine resolvable designs, confirming a conjecture and advancing understanding of their spectral properties.

Contribution

It provides the first explicit calculation of distance signatures for these designs, proving a conjecture by Kohei Yamada.

Findings

Distance signatures of incidence matrices are explicitly determined.

The conjecture by Kohei Yamada is proved.

Advances spectral analysis of affine resolvable designs.

Abstract

In this note, we determined the distance signatures of the incidence matrices of affine resolvable designs. This proves a conjecture by Kohei Yamada.