A duality of scaffolds for translation association schemes
Combinatorics
2022-01-05 v2
Abstract
Scaffolds are certain tensors arising in the study of association schemes, and have been (implicitly) understood diagrammatically as digraphs with distinguished "root" nodes and with matrix edge weights, often taken from Bose-Mesner algebras. In this paper, we first present a slight modification of Martin's conjecture (2021) concerning a duality of scaffolds whose digraphs are embedded in a closed disk in the plane with root nodes all lying on the boundary circle, and then show that this modified conjecture holds true if we restrict ourselves to the class of translation association schemes, i.e., those association schemes that admit abelian regular automorphism groups.
Keywords
Cite
@article{arxiv.2110.15848,
title = {A duality of scaffolds for translation association schemes},
author = {Xiaoye Liang and Ying-Ying Tan and Hajime Tanaka and Tao Wang},
journal= {arXiv preprint arXiv:2110.15848},
year = {2022}
}
Comments
13 pages