TY - JOUR

T1 - Algebraic combinatorics in mathematical chemistry. Methods and algorithms. I. Permutation groups and coherent (cellular) algebras.

AU - Klin, Mikhail

AU - Rücker, Christoph

AU - Rücker, Gerta

AU - Tinhofer, Gottfried

PY - 1999/10/1

Y1 - 1999/10/1

N2 - Let (G, Ω) be a permutation group of degree n. Let V(G, Ω) be the set of all square matrices of order n which commute with all permutation matrices corresponding to permutations from (G, Ω). V(G, Ω) is a matrix algebra which is called the centralizer algebra of (G, Ω). In this paper we introduce the combinatorial analogue of centralizer algebras, namely coherent (cellular) algebras and consider the properties of these algebras. It turns out that coherent algebras provide a very helpful tool for the investigation of the symmetries of graphs of different kinds, in particular, of molecular graphs.

AB - Let (G, Ω) be a permutation group of degree n. Let V(G, Ω) be the set of all square matrices of order n which commute with all permutation matrices corresponding to permutations from (G, Ω). V(G, Ω) is a matrix algebra which is called the centralizer algebra of (G, Ω). In this paper we introduce the combinatorial analogue of centralizer algebras, namely coherent (cellular) algebras and consider the properties of these algebras. It turns out that coherent algebras provide a very helpful tool for the investigation of the symmetries of graphs of different kinds, in particular, of molecular graphs.

KW - Chemistry

KW - Mathematics

UR - http://www.scopus.com/inward/record.url?scp=0002261718&partnerID=8YFLogxK

M3 - Journal articles

VL - 40

SP - 7

EP - 138

JO - MATCH Communications in mathematical and in computer chemistry

JF - MATCH Communications in mathematical and in computer chemistry

SN - 0340-6253

ER -