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Products of class operators of the symmetric group
Author(s) -
Katriel Jacob
Publication year - 1989
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560350402
Subject(s) - conjecture , class (philosophy) , mathematics , operator (biology) , product (mathematics) , group (periodic table) , combinatorics , pure mathematics , physics , chemistry , quantum mechanics , computer science , geometry , biochemistry , repressor , artificial intelligence , transcription factor , gene
A combinatorial derivation of the product of the class of three cycles, [(1) N−3 (3)] N with an arbitrary class operator of the symmetric group S N is presented. The form of this result suggests a conjecture concerning the expression of the general class operator product in terms of a relatively small number of reduced class coefficients. The conjecture is applied to the determination of the products of [(1) N −4 (4)] N , [(1) N −4 (2) 2 ] N , and [(1) N −5 (5)] N with arbitrary class operators. General expressions for the reduced class coefficients of the simplest type are obtained.