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Eigenvalues of single‐cycle class‐sums in the symmetric group. II
Author(s) -
Katriel Jacob,
Pauncz Ruben
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.560480205
Subject(s) - mathematics , eigenvalues and eigenvectors , symmetric group , conjecture , sums of powers , representation theory of the symmetric group , class (philosophy) , combinatorics , group (periodic table) , representation (politics) , diagram , pure mathematics , power sum symmetric polynomial , orthogonal polynomials , classical orthogonal polynomials , macdonald polynomials , physics , computer science , quantum mechanics , statistics , artificial intelligence , politics , political science , law
Explicit expressions for the eigenvalues of the single‐cycle class‐sums [( p )(1) n – p ] n of the symmetric group ( S n ), with p ≤ 20, are constructed. A new algorithm is used that makes no use of representation‐theoretic data. The expressions obtained consist of polynomials in the symmetric power‐sums over the “contents” of the Young diagram specifying the irreducible representation, with coefficients that are polynomials in n . On the basis of the results obtained for p ≤ 20, a conjecture is proposed concerning the general form of the four leading terms in these polynomials. © 1993 John Wiley & Sons, Inc.