A duality of scaffolds for translation association schemes

Xiaoye Liang, Ying Ying Tan, Hajime Tanaka, Tao Wang

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)110-124
Number of pages15
JournalLinear Algebra and Its Applications
Publication statusPublished - 2022 Apr 1


  • Association scheme
  • Bose–Mesner algebra
  • Duality
  • Scaffold
  • Tensor

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics


Dive into the research topics of 'A duality of scaffolds for translation association schemes'. Together they form a unique fingerprint.

Cite this