Paul Terwilliger

activity

20242026

collaborators

7 papers

math.CO2026

Variations on a circular Hessenberg pair

Kazumasa Nomura, Paul Terwilliger

A square matrix is called Hessenberg whenever each entry below the subdiagonal is zero and each entry on the subdiagonal is nonzero. A Hessenberg pair is an ordered pair of diagona…

math.CO2026

Circular Hessenberg pairs and the tridiagonal relations

Kazumasa Nomura, Paul Terwilliger

A square matrix is said to be Hessenberg whenever each entry below the subdiagonal is zero, and each entry on the subdiagonal is nonzero. A Hessenberg matrix is called circular whe…

math.CO2026

Strengthening the balanced set condition for the distance-regular graph of the bilinear forms

Paul Terwilliger, Jason Williford

We consider a distance-regular graph $I^ = (X, R)$ called the bilinear forms graph $H_{q} (D, N - D)$ ; we assume $N > 2 D \geq 6$ and $q \neq = 2$ . We show that $I^$ satisfies the follo…

math.CO2025

An equitable partition for the distance-regular graph of the bilinear forms

Paul Terwilliger, Jason Williford

We consider a type of distance-regular graph $I^ = (X, R)$ called a bilinear forms graph. We assume that the diameter $D$ of $I^$ is at least $3$ . Fix adjacent vertices $x,y…

math.CO2025

Raising and lowering maps for tridiagonal pairs

Paul Terwilliger

Let $V$ denote a nonzero finite-dimensional vector space. A tridiagonal pair on $V$ is an ordered pair $A, A^{*}$ of maps in $End (V)$ such that (i) each of $A, A^{*}$ is diagonal…

math.CO2025

2-Homogeneous bipartite distance-regular graphs and the quantum group $U_{q}^{'} (so_{6})$

Paul Terwilliger

We consider a 2-homogeneous bipartite distance-regular graph $I^$ with diameter $D \geq 3$ . We assume that $I^$ is not a hypercube nor a cycle. We fix a $Q$ -polynomial ordering of…

Variations on a circular Hessenberg pair

Circular Hessenberg pairs and the tridiagonal relations

Strengthening the balanced set condition for the distance-regular graph of the bilinear forms

An equitable partition for the distance-regular graph of the bilinear forms

Raising and lowering maps for tridiagonal pairs

2-Homogeneous bipartite distance-regular graphs and the quantum group Uq′​(so6​)

2-Homogeneous bipartite distance-regular graphs and the quantum group $U_{q}^{'} (so_{6})$