Related papers: On a Compact Generalization of Association Schemes
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…
We propose the notion of association schemoids generalizing that of association schemes from small categorical points of view. In particular, a generalization of the Bose-Mesner algebra of an association scheme appears as a subalgebra in…
We give a definition of associative schemes, schemes of associative rings, over a field $k,$ using the definition of completion of an associative $k$-algebra in a finite set of simple modules. We start by giving a weaker but sufficient…
We show that taking the set of primitive idempotents of commutative association schemes is a functor from the category of commutative association schemes with surjective morphisms to the category of finite sets with surjective partial…
A schemoid is a generalization of association schemes from the point of view of small categories. In this article, we discuss schemoid structures for two kinds of small categories; the canonical small category defined by a poset, and…
We propose a homology theory for locally compact spaces with ends in which the ends play a special role. The approach is motivated by results for graphs with ends, where it has been highly successful. But it was unclear how the original…
In recent work, the authors developed a simple method of constructing topological spaces from certain well-behaved partially ordered sets -- those coming from sequences of relations between finite sets. This method associates a given poset…
In the authors book, Associative Algebraic Geometry, 2023, and the following article Shemes of Associative Algebras,\\ https://doi.org/10.48550/arXiv.2410.17703,2024, we use an algebraization of the semi-local formal moduli of simple…
In this paper, for any prime $p$, we propose the notion of a $p$-transitive association scheme. This notion aims to generalize the fact that the regular module of a group algebra of a finite group has a unique trivial submodule to the case…
Compact sets in constructive mathematics capture our intuition of what computable subsets of the plane (or any other complete metric space) ought to be. A good representation of compact sets provides an efficient means of creating and…
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…
We define a class of spaces on which one may generalise the notion of compactness following motivating examples from higher-dimensional number theory. We establish analogues of several well-known topological results (such as Tychonoff's…
We introduce the coherent algebra of a compact metric measure space by analogy with the corresponding concept for a finite graph. As an application we show that upon topologizing the collection of isomorphism classes of compact metric…
Compact representations of objects is a common concept in computer science. Automated planning can be viewed as a case of this concept: a planning instance is a compact implicit representation of a graph and the problem is to find a path (a…
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 introduce the concept of compact quantitative equational theory. A quantitative equational theory is defined to be compact if all its consequences are derivable by means of finite proofs. We prove that the theory of interpolative…
This survey purports to be an elementary introduction to compactly presented groups, which are the analogue of finitely presented groups in the broader realm of locally compact groups. In particular, compact presentation is interpreted as a…
We construct a wide subcategory of the category of finite association schemes with a collection of desirable properties. Our subcategory has a first isomorphism theorem analogous to that of groups. Also, standard constructions taking…
Association schemes form one of the main objects of algebraic combinatorics, classically defined on finite sets. In this paper we define association schemes on arbitrary, possibly uncountable sets with a measure. We study operator…
Association schemes were originally introduced by Bose and his co-workers in the design of statistical experiments. Since that point of inception, the concept has proved useful in the study of group actions, in algebraic graph theory, in…