In this paper, we prove the following two theorems. Theorem 1 Let 0 denote a distance-regular graph with diameter d â‰¥ 3. Suppose E and F are primitive idempotents of 0, with cosine sequences Ïƒ0, Ïƒ1,â€¦ (More)

In this paper, we prove the following: Theorem. Let A= ã€ˆA0; A1; : : : ; Adã€‰ denote a complex character algebra with dÂ¿ 2 which is P-polynomial with respect to the ordering A0; A1; : : : ; Ad of theâ€¦ (More)

Ito, Tanabe and Terwilliger recently introduced the notion of a tridiagonal pair. We apply their results to distance-regular graphs and obtain the following theorem. THEOREM. Let denote aâ€¦ (More)

A k-arc in a (finite) projective plane n,, of order n is a set of k points, no three of which are collinear. The maximum k for which there exist k-arcs in Ed, is n + 1 if n is odd, and n + 2 if n isâ€¦ (More)

We display an action of the tetrahedron algebra on the standard module for any Hamming graph or Doob graph. To do this, we use some results of Brian Hartwig concerning tridiagonal pairs of Krawtchoukâ€¦ (More)