Related papers: Properties of Commutative Association Schemes deri…
We give a full description of the algebraic structures of the Bose-Mesner algebra and Terwilliger algebra of the wreath product of one-class association schemes.
We introduce generalised orbit algebras. The purpose here is to measure how some combinatorial properties can characterize the action of a group of permutations on the subsets. The similarity with orbit algebras is such that it took the…
For an efficient implementation of Buchberger's Algorithm, it is essential to avoid the treatment of as many unnecessary critical pairs or obstructions as possible. In the case of the commutative polynomial ring, this is achieved by the…
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…
In [3], Hanaki defined the Terwilliger algebras of association schemes over a commutative unital ring. In this paper, we call the Terwilliger algebras of association schemes over a field $\mathbb{F}$ the Terwilliger $\mathbb{F}$-algebras of…
In this paper we will prove that there exists a covariant functor from the category of schemes to the category of graphs. This functor provides a combination between algebraic varieties and combinatorial graphs so that the invariants…
The paper presents a novel software framework for Association Rule Mining named uARMSolver. The framework is written fully in C++ and runs on all platforms. It allows users to preprocess their data in a transaction database, to make…
The Terwilliger algebras of association schemes over an arbitrary field $\mathbb{F}$ were called the Terwilliger $\mathbb{F}$-algebras of association schemes in [9]. In this paper, we study the Terwilliger $\mathbb{F}$-algebras of factorial…
A simple algorithm is proposed for constructing generators of gauge symmetry as well as reducibility relations for arbitrary systems of field equations in two dimensions.
Many statistical models are algebraic in that they are defined by polynomial constraints or by parameterizations that are polynomial or rational maps. This opens the door for tools from computational algebraic geometry. These tools can be…
Cluster algebras have recently become an important player in mathematics and physics. In this work, we investigate them through the lens of modern data science, specifically with techniques from network science and machine learning. Network…
In this article, we focus on association schemes with some properties derived from the orbitals of a transitive permutation group $G$ with a one-point stabilizer $H$ satisfying $H <N_G(H)<N_G(N_G(H))\unlhd G$ and $|N_G(N_G(H))|=p^3$ where…
The main idea in this paper is merging two techniques that have been recently developed. On the one hand, we consider MCCGS, standing for Minimal Canonical Comprehensive Groebner Systems, a recently introduced computational tool yielding…
Symmetric strongly shifted ideals are a class of monomial ideals which come equipped with an action of the symmetric group and are analogous to the well-studied class of strongly stable monomial ideals. In this paper we focus on algebraic…
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…
Spectrum generating algebras are used in various fields of physics as models to determine quantum structure, including energy levels and transition strengths. The advantage of such models is that their group structure allows an extensive…
We study the symmetry properties of autonomous integrating factors from an algebraic point of view. The symmetries are delineated for the resulting integrals treated as equations and symmetries of the integrals treated as functions or…
In this paper, we introduce the category of blueprints, which is a category of algebraic objects that include both commutative (semi)rings and commutative monoids. This generalization allows a simultaneous treatment of ideals resp.\…
We can define the adjacency algebra of an association scheme over arbitrary field. It is not always semisimple over a field of positive characteristic. The structures of adjacency algebras over a field of positive characteristic have not…
Motivated by the combinatorial properties of products in Lie algebras, we investigate the subset of permutations that naturally appears when we write the long commutator $[x_1, x_2, ..., x_m]$ as a sum of associative monomials. We…