ﻻ يوجد ملخص باللغة العربية
{Let ${Cal X}$ be a self-dual P-polynomial association scheme. Then there are at most 12 diagonal matrices $T$ such that $(PT)^3=I$. Moreover, all of the solutions for the classical infinite families of such schemes (including the Hamming scheme) are classified.
An association scheme is called quasi-thin if the valency of each its basic relation is one or two. A quasi-thin scheme is Kleinian if the thin residue of it forms a Klein group with respect to the relation product. It is proved that any Kleinian sch
In this paper we aim to characterize association schemes all of whose symmetric fusion schemes have only integral eigenvalues, and classify those obtained from a regular action of a finite group by taking its orbitals.
We construct twelve infinite families of pseudocyclic and non-amorphic association schemes, in which each nontrivial relation is a strongly regular graph. Three of the twelve families generalize the counterexamples to A. V. Ivanovs conjecture by Ikuta and Munemasa [15].
In this paper we characterize large regular graphs using certain entries in the projection matrices onto the eigenspaces of the graph. As a corollary of this result, we show that large association schemes become $P$-polynomial association schemes. Ou
We utilize association schemes to analyze the quality of semidefinite programming (SDP) based convex relaxations of integral packing and covering polyhedra determined by matchings in hypergraphs. As a by-product of our approach, we obtain bounds on t