Related papers: Association Scheme on Triples from the Unitary Gro…
A geometrical pattern is a set of points with all pairwise distances (or, more generally, relative distances) specified. Finding matches to such patterns has applications to spatial data in seismic, astronomical, and transportation…
It is proved that association schemes with bipartite basis graphs are exactly 2-schemes. This result follows from a characterization of p-schemes for an arbitrary prime p in terms of basis digraphs.
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…
With each piecewise monotonic map of the unit interval, a dimension triple is associated. The dimension triple, viewed as a Z[t, t^{-1}] module, is finitely generated, and generators are identified. Dimension groups are computed for Markov…
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…
Random intersection graphs model networks with communities, assuming an underlying bipartite structure of groups and individuals, where these groups may overlap. Group memberships are generated through the bipartite configuration model.…
Partial connections are (singular) differential systems generalizing classical connections on principal bundles, yielding analogous decompositions for manifolds with nonfree group actions. Connection forms are interpreted as maps…
This paper introduces a description of Endomorphisms of the translation group in an affine plane, will define the addition and composition of the set of endomorphisms and specify the neutral elements associated with these two actions and…
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…
This paper proposes an agent-based model which reproduces different structures of animal groups. The shape and structure of the group is the effect of simple interaction rules among individuals: each animal deploys itself depending on the…
This paper investigates the mining of class association rules with rough set approach. In data mining, an association occurs between two set of elements when one element set happen together with another. A class association rule set (CARs)…
Ternary coherent configurations are, on the one hand, a special case of multidimensional coherent configurations introduced by L. Babai (2016), and, on the other hand, a natural generalization of association schemes on triples introduced by…
A relation algebra is called measurable when its identity is the sum of measurable atoms, and an atom is called measurable if its square is the sum of functional elements. In this paper we show that atomic measurable relation algebras have…
A capsule is a group of neurons whose activity vector represents the instantiation parameters of a specific type of entity such as an object or an object part. We use the length of the activity vector to represent the probability that the…
If $G$ is a finite group then there is an integer $M_G$ such that$,$ for $u\ge M_G$ and $u\equiv 1$ or $3$ (mod 6), there is a Steiner triple system $U$ on $u$ points for which ${\rm Aut} U \cong G. \ $ If $V$ is a Steiner triple system…
Given two associative algebras A, C and a linear space V together with some linear maps R_1, R_2, R_3, E satisfying some conditions, we define an associative algebra structure on A\otimes V\otimes C called a two-sided crossed product.…
In this paper, we obtain some new results on closed subschemes. Specially, we define natural addition and multiplication on the closed subschemes of a scheme. It is shown that "the multiplication" precisely coincides with the well known…
In the preprint arXiv:2511.07900 we proved that there exists a localizing ring $A_M$ for $A$ an associative ring with unit, and $M=\oplus_{i=1}^rM_i$ a direct sum of $r\geq 1$ simple right $A$-modules. For a homomorphism of associative…
A triangle presentation is a combinatorial datum that encodes the action of a group on a $2$-dimensional triangle complex with prescribed links, which is simply transitive on the vertices. We provide the first infinite family of triangle…
We introduce a linear algebraic object called a bidiagonal triad. A bidiagonal triad is a modification of the previously studied and similarly defined concept of bidiagonal triple. A bidiagonal triad and a bidiagonal triple both consist of…