Algebraic Combinatorics in Mathematical Chemistry. Methods and Algorithms. I. Permutation Groups and Coherent (cellular) Algebras

I . Permutation Groups and Coherent ( Cellular ) Algebras

The remoteness of the permutation code of the group $U_{6n}$

Recently, a new parameter of a code, referred to as the remoteness, has been introduced.This parameter can be viewed as a dual to the covering radius. It is exactly determined for the cyclic and dihedral groups. In this paper, we consider the group $U_{6n}$ as a subgroup of $S_{2n+3}$ and obtain its remoteness.  We show that the remoteness of the permutation code $U_{6n}$ is $2n+2$.  Moreover, ...

ON HIGH CLOSED CELLULAR ALGEBRASAND HIGH CLOSED ISOMORPHISMSSapienti

We study m-closed cellular algebras (coherent connguration) and m-isomorphisms of cellular algebras which can be regarded as mth approximations to Schurian algebras (i.e. the centralizer algebras of permutation groups) and to strong isomorphisms (i.e. bijections of the point sets taking one algebra to the other) respectively. If m = 1 we come to arbitrary cellular algebras and their weak isomor...

Semisimplicity of Cellular Algebras over Positive Characteristic Fields

In this paper, we investigate semisimplicity of cellular algebras over positive characteristic fields. Our main result shows that the Frame number of cellular algebras characterizes semisimplicity of it. In a sense, this is a generalization of Maschke’s theorem. 1. intrudoction Cellular algebras are an object in algebraic combinatorics which were introduced by B. Yu. Weisfeiler and A. A. Lehman...

Coherent configurations

In Section 2, after giving the basic definitions and some elementary consequences, we introduce two fundamental algebraic structures associated with a coherent configuration, namely, the boolean algebra of admissable relations and the adjacency ring. The action of a group on a finite set induces the structure of a coherent configuration in the set, and in this situations, which we refer to as t...