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Products of class‐sums of the symmetric group: Generalizing the recurrence relations
Author(s) -
Katriel Jacob
Publication year - 1993
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.560470402
Subject(s) - symmetrization , class (philosophy) , recurrence relation , mathematics , symmetric group , group (periodic table) , pure mathematics , combinatorics , algebra over a field , physics , quantum mechanics , computer science , artificial intelligence
The formulation of a combinatorial theory of the structure of the class‐algebra of the symmetric group is pursued. Recurrence relations for reduced class‐coefficients involving imbedded cycles are presented. It is pointed out that for bridging cycles one can obtain elimination rules that involve symmetrization over sets of reduced class‐coefficients with common cycle‐structures but inequivalent index distributions. Consequently, some of these reduced class‐coefficients remain individually inaccessible. © 1993 John Wiley & Sons, Inc.