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Products of class sums of the symmetric group: Rules of partial elimination

✍ Scribed by Jacob Katriel

Publisher: John Wiley and Sons
Year: 1997
Tongue: English
Weight: 218 KB
Volume: 63
Category: Article
ISSN: 0020-7608
DOI: 10.1002/(sici)1097-461x(1997)63:5<961::aid-qua6>3.0.co;2-u

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✦ Synopsis

Progress in the formulation of a procedure for the combinatorial evaluation of the product of a single-cycle and an arbitrary class sum in the symmetric group algebra is presented. The procedure consists of a ''global conjecture'' concerning wŽ .x w x the representation of the product p и ) in terms of a set of operators referred to as n n Ž . reduced class sums, and of an incomplete set of rules for the evaluation of the Ž . n -independent! coefficients of these operators. Two new types of index elimination rules are suggested, and some properties of the formalism are explored. These include useful sum rules as well as a certain ''detailed balance'' property that sheds some light on a combinatorial aspect of the global conjecture. The present results account for several new types of reduced class coefficients and suggest some feasible further developments. Some outstanding open problems are pointed out.

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