More on the Terwilliger algebra of Johnson schemes

TL;DR

This paper completes the characterization of the Terwilliger algebra for Johnson schemes by analyzing the case where 2d ≤ n < 3d, extending previous results that covered n ≥ 3d.

Contribution

It provides a complete description of the Terwilliger algebra of Johnson schemes for all parameter ranges, filling a gap in existing literature.

Findings

Determined the Terwilliger algebra for 2d ≤ n < 3d.

Extended the classification of Johnson schemes.

Provided algebraic structures for previously unresolved cases.

Abstract

In [F. Levstein, C. Maldonado, The Terwilliger algebra of the Johnson schemes, Discrete Math. 307 (2007) 1621--1635], the Terwilliger algebra of the Johnson scheme $J(n,d)$ was determined when $n\geq 3d$. In this paper, we determine the Terwilliger algebra ${\mathcal T}$ for the remaining case $2d\leq n<3d$.