Related papers: Circulant association schemes on triples

Association schemes play an important role in algebraic combinatorics and have important applications in coding theory, graph theory and design theory. The methods to construct association schemes by using bent functions have been…

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…

Recurrence is a fundamental characteristic of dynamical systems with complicated behavior. Understanding the inner structure of recurrence is challenging, especially if the system has many degrees of freedom and is subject to noise. We…

In this paper three Schur ring are discussed, namenly: Hamming, circulant orbists and decimated circulant orbits Schur ring. By using autocorrelation function and the run structure of binary sequences we proof the relation between this…

The paper provides an introduction to the field of Algebraic Set Theory (AST). AST is a flexible categorical framework for studying different kinds of set theories: both classical and constructive, predicative and impredicative. We discuss…

This paper characterizes hierarchical clustering methods that abide by two previously introduced axioms -- thus, denominated admissible methods -- and proposes tractable algorithms for their implementation. We leverage the fact that, for…

We prove that every finite arc-transitive graph of valency twice a prime admits a nontrivial semiregular automorphism, that is, a non-identity automorphism whose cycles all have the same length. This is a special case of the Polycirculant…

The group $PGL(2,q)$ has an embedding into $PGL(3,q)$ such that it acts as the group fixing a nonsingular conic in $PG(2,q)$. This action affords a coherent configuration $R(q)$ on the set $L(q)$ of non-tangent lines of the conic. We show…

We study associative multiplications in semi-simple associative algebras over C compatible with the usual one or, in other words, linear deformations of semi-simple associative algebras over C. It turns out that these deformations are in…

We introduce a notion of compact association schemes, which serves as a compact analogue of classical (finite) association schemes. Our definition is formulated in a way that closely parallels the finite case, naturally admits a…

Let ${\cal M}$ denote the Bose--Mesner algebra of a commutative $d$-class association scheme ${\mathfrak X}$ (not necessarily symmetric), and $\Gamma$ denote a (strongly) connected (directed) graph with adjacency matrix $A$. Under the…

We introduce two refinements of the class of $5/2$-groups, inspired by the classes of automorphism groups of configurations and automorphism groups of unit circulant digraphs. We show that both of these classes have the property that any…

Freudenthal triple systems come in two flavors, degenerate and nondegenerate. The best criterion for distinguishing between the two which is available in the literature is by descent. We provide an identity which is satisfied only by…

Inspired by the ideas and techniques used in the study of cluster algebras we construct a new class of algebras, called bistellar cluster algebras, from closed oriented triangulated even-dimensional manifolds by performing…

Association schemes are combinatorial objects that allow us solve problems in several branches of mathematics. They have been used in the study of permutation groups and graphs and also in the design of experiments, coding theory, partition…

In this paper, we begin by partitioning the edges (or arcs) of a circulant (di)graph according to which generator in the connection set leads to each edge. We then further refine the partition by subdividing any part that corresponds to an…

Classical finite association schemes lead to a finite-dimensional algebras which are generated by finitely many stochastic matrices. Moreover, there exist associated finite hypergroups. The notion of classical discrete association schemes…

This is an overview of the idea of a crossed module. For a group, the triple that consists of the group, its group of automorphisms, and the canonical homomorphism from the group to its group of automorphisms constitutes a crossed module.…

Terwilliger algebras are a subalgebra of a matrix algebra constructed from an association scheme. Rie Tanaka defined what it means for a Terwilliger algebra to be almost commutative and gave five equivalent conditions. In this paper we…

An association scheme is called amorphic if every possible fusion of relations gives rise to another association scheme. In earlier work, we showed that if an association scheme has at most one relation that is neither strongly regular of…