ISSN:
0020-7608
Keywords:
Symmetric group
;
class-sums
;
Chemistry
;
Theoretical, Physical and Computational Chemistry
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Chemistry and Pharmacology
Notes:
An algorithm for the evaluation of the structure constants in the class algebra of the symmetric group has recently been considered. The product of the class sum [(p)]n that consists of a cycle of length p and n-p fixed points, with an arbitrary class sum in Sn, was found to be expressible in terms of a set of reduced class coefficients (RCCs), the p-RCCs. The combinatorial significance of the p-RCCs is elucidated, showing that they are related to a well-defined enumeration problem within Sp, which has to do with a certain refinement of the corresponding class multiplication problem. This is in contrast with the representation-theoretic evaluation of the p-RCCs, which requires the evaluation of products involving [(p)]n for several values of n 〉 p. The combinatorial interpretation of the p-RCCs allows the derivation of some of their previously conjectured properties and of some of the “elimination rules” that specific types of p-RCCs were found to satisfy. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 68: 103-118, 1998
Type of Medium:
Electronic Resource
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