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Unit subduced cycle indices for combinatorial enumeration
Author(s) -
Fujita Shinsaku
Publication year - 1994
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.3190180407
Subject(s) - enumeration , coset , mathematics , combinatorics , table (database) , unit (ring theory) , key (lock) , computer science , data mining , mathematics education , computer security
Combinatorial enumeration by means of unit subduced cycle indices (USCIs) is discussed by using the group I ( A 5 ) and the related groups as examples. A modified method for the derivation of USCIs is presented, where a subduced mark table is a key concept. Several properties of USCIs are discussed by clarifying the relationship between double cosets and the subduction of coset representations, which gives an alternative formulation of the USCIs. This treatment provides us with a new prospect concerning the properties of double cosets. The usefulness of subduced cycle indices and cycle indices derived from USCIs is exemplified by enumeration based on an icosahedron.