Related papers: Three-class association schemes from cyclotomy
An association scheme is called skew-symmetric if it has no symmetric adjacency relations other than the diagonal one. In this paper, we study 4-class skew-symmetric association schemes. In J. Ma [On the nonexistence of skew-symmetric…
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. Ivanov's…
An association scheme on triples (AST) is a three-dimensional analogue of a classical association scheme. Similar to how a transitive group action produces a Schurian classical association scheme, a two-transitive group action produces an…
We classify the symmetric association schemes with faithful spherical embedding in 3-dimensional Euclidean space. Our result is based on previous research on primitive association schemes with $m_1 = 3$.
It is well-known that translation schemes on prime number of vertices are exactly the cyclotomic schemes. In this current paper, we show that there are no nonsymmetric primitive translation schemes on prime square vertices with at most four…
Let X be a pseudocyclic association scheme in which all the nontrivial relations are strongly regular graphs with the same eigenvalues. We prove that the principal part of the first eigenmatrix of X is a linear combination of an incidence…
In this paper, we construct an infinite series of 9-class association schemes from a refinement of the partition of Delsarte-Goethals codes by their Lee weights. The explicit expressions of the dual schemes are determined through direct…
In this paper, the association scheme defined on the flags of a finite generalized quadrangle is considered. All possible fusions of this scheme are listed, and a full description for those of classes 2 and 3 is given. Furthermore, it is…
In this paper, we obtain classification results for higher-dimensional analogues of classical association schemes called association schemes on triples (ASTs). We present an algorithm that enumerates all ASTs on a fixed number of vertices…
We present the tables of feasible parameters of primitive $3$-class $Q$-polynomial association schemes and $4$- and $5$-class $Q$-bipartite association schemes (on up to $2800$, $10000$, and $50000$ vertices, respectively), accompanied by a…
Using cyclotomic classes of order twelve for certain finite fields, we construct an infinite family of almost difference sets and normally regular graphs applying the theory of cyclotomy. We show that in each of these fields neither the…
Association schemes on triples (ASTs) are 3-dimensional analogues of classical association schemes. If a group acts two-transitively on a set, the orbits of the action induced on the triple Cartesian product of that set yields an AST. By…
Leading towards the classification of primitive commutative association schemes as the ultimate goal, Bannai and some of his school have been trying to * identify the major sources of (primitive) commutative association schemes, * collect…
We show an inequality involving the third largest or second smallest dual eigenvalues of $Q$-polynomial association schemes of class at least three. Also we characterize dual-tight $Q$-polynomial association schemes of class three. Our…
Association schemes on triples (ASTs) are ternary analogues of classical association schemes, whose relations and adjacency algebras are ternary instead of binary. We provide a survey of the current progress in the study of ASTs,…
We classify certain non-symmetric commutative association schemes. As an application, we determine all the primitive weakly distance-regular circulant digraphs.
We introduce a concept of cyclotomic association scheme C over a finite near-field. It is proved that if C is nontrivial, then Aut(C)<AGL(V) where V is the linear space associated with the near-field. In many cases we are able to get more…
Here we describe three straightforward examples of what was called a graphic Fourier transformation in [4]. At least two of these examples may be viewed simply as monoidal comonads on suitable monoidal closed functor categories, but the…
In this paper, we give a characterization of the class of all circular-arc graphs whose schemes are association. Moreover, all association schemes which are the scheme of a circular-arc graph are characterized, specially it is proved that…