Paul Terwilliger

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20242026

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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 $Γ = (X, R)$ called the bilinear forms graph $H_{q} (D, N - D)$ ; we assume $N > 2 D \geq 6$ and $q \neq = 2$ . We show that $Γ$ satisfies the followi…

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…