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A Logarithmic Connection for Circular Permutation Enumeration
Author(s) -
Goulden I. P.,
Jackson D. M.
Publication year - 1984
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm1984702121
Subject(s) - enumeration , mathematics , logarithm , permutation (music) , connection (principal bundle) , combinatorics , rotation (mathematics) , generating function , discrete mathematics , mathematical analysis , geometry , physics , acoustics
A general theorem is obtained for the enumeration of permutations equivalent under cyclic rotation. This result gives the generating function as the logarithm of a determinant which arises in the enumeration of a related linear permutation enumeration. Applications of this theorem are given to a number of classical enumerative problems.