A $Q$-polynomial structure associated with the projective geometry $L_N(q)$

Abstract

There is a type of distance-regular graph, said to be $Q$-polynomial. In this paper we investigate a generalized $Q$-polynomial property involving a graph that is not necessarily distance-regular. We give a detailed description of an example associated with the projective geometry $L_N(q)$.

21 pages

Cited by in corpus (4)

• A $Q$-polynomial structure for the Attenuated Space poset ${\mathcal{A}}_q(N,M)$
• The nucleus of a $Q$-polynomial distance-regular graph
• A $q$-version of the relation between the hypercube, the Krawtchouk chain and Dicke states
• Projective geometries, $Q$-polynomial structures, and quantum groups