Paul M. Terwilliger

activity

20012005

P

-and

Q

-polynomial association schemes

40 citations · 120 across the 22 of their papers we have counts for

collaborators

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7 papers · 1 filter

math.CO2005★ 1 cited

Taut distance-regular graphs and the subconstituent algebra

Mark S. MacLean, Paul Terwilliger

We consider a bipartite distance-regular graph $G$ with diameter $D$ at least 4 and valency $k$ at least 3. We obtain upper and lower bounds for the local eigenvalues of $G$ in ter…

math.CO2004★ 40 cited

Some algebra related to $P$ -and $Q$ -polynomial association schemes

Tatsuro Ito, Kenichiro Tanabe, Paul Terwilliger

Let $K$ denote a field, and let $V$ denote a vector space over $K$ with finite positive dimension. Consider a pair of linear transformations $A : V \to V$ and $A^{*} : V \to V$ that satisf…

math.CO2003

The Pseudo Cosine Sequences of a Distance-Regular Graph

Arlene A. Pascasio, Paul Terwilliger

Let $G$ denote a distance-regular graph with diameter $D \geq 3$ , valency $k$ , and intersection numbers $a_{i}$ , $b_{i}$ , $c_{i}$ . By a {\it pseudo cosine sequence} of $G$ we mean a sequen…

math.CO2003

An inequality for regular near polygons

Paul Terwilliger, Chih-wen Weng

Let $G$ denote a near-polygon distance-regular graph with diameter $d \geq 3$ , valency $k$ and intersection numbers $a_{1} > 0$ , $c_{2} > 1$ . Let $θ_{1}$ denote the second largest eigenvalue…

math.CO2003

Distance-regular graphs, pseudo primitive idempotents, and the Terwilliger algebra

Paul Terwilliger, Chih-wen Weng

Let $Γ$ denote a distance-regular graph with diameter $D \geq 3$ and Bose-Mesner algebra $M$ . For $θ \in C \cup \infty$ we define a 1 dimensional subspace of $M$ which we call $M (θ)$ .…

math.CO2003★ 1 cited

The displacement and split decompositions for a $Q$ -polynomial distance-regular graph

Paul Terwilliger

Let $Γ$ denote a $Q$ -polynomial distance-regular graph with diameter at least three and standard module $V$ . We introduce two direct sum decompositions of $V$ . We call these the di…

Taut distance-regular graphs and the subconstituent algebra

Some algebra related to P-and Q-polynomial association schemes

The Pseudo Cosine Sequences of a Distance-Regular Graph

An inequality for regular near polygons

Distance-regular graphs, pseudo primitive idempotents, and the Terwilliger algebra

The displacement and split decompositions for a Q-polynomial distance-regular graph

Some algebra related to $P$ -and $Q$ -polynomial association schemes

The displacement and split decompositions for a $Q$ -polynomial distance-regular graph