The Terwilliger algebra of the incidence graphs of Johnson geometry

TL;DR

This paper determines the Terwilliger algebra of the incidence graph of Johnson geometry for certain parameters, providing explicit bases and dimension, extending previous work on Johnson schemes.

Contribution

It explicitly computes the Terwilliger algebra of the incidence graph of Johnson geometry for 3m ≤ n, including bases and dimension, which was not previously known.

Findings

Explicit bases of the algebra are provided.

The dimension of the algebra is calculated.

The results extend previous work on Johnson schemes.

Abstract

Levstein and Maldonado [F. Levstein, C. Maldonado, The Terwilliger algebra of the Johnson schemes, Discrete Mathematics 307 (2007) 1621--1635] computed the Terwilliger algebra of the Johnson scheme $J(n,m)$ when $3m\leq n$. In this paper, we determine the Terwilliger algebra of the incidence graph $J(n,m,m+1)$ of Johnson geometry when $3m\leq n$, give two bases of this algebra, and calculate its dimension.