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

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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.

Original languageEnglish
JournalMATCH Communications in mathematical and in computer chemistry
Volume40
Pages (from-to)7-138
Number of pages132
ISSN0340-6253
Publication statusPublished - 01.10.1999
Externally publishedYes

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