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Theoretical Chemistry Accounts

, Volume 101, Issue 6, pp 409–420 | Cite as

Möbius function and characteristic monomials for combinatorial enumeration

  • Shinsaku Fujita
Regular article

Abstract.

After the definitions of amplified representations and number-theoretical vectors, the markaracter table of a cyclic subgroup is converted into the corresponding Q-conjugacy character table. The conversion is shown to necessitate an interconversion matrix that contains Möbius functions as elements. Since the interconversion matrix gives characteristic monomials for cyclic groups, all the powers appearing in each of the characteristic monomials are shown to be integers. Characteristic monomials for finite groups are then built up by starting from those of cyclic groups. This procedure clarifies the fact that all the powers appearing in each characteristic monomial for finite groups are integers. The relationship between characteristic monomial tables and unit-subduced-cycle-index tables is discussed with respect to their application to isomer enumeration.

Key words:Q-conjugacy character Characteristic monomial Möbius function Enumeration Group 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Shinsaku Fujita
    • 1
  1. 1.Department of Chemistry and Materials Technology, Kyoto Institute of Technology, Matsugasaki, Sakyoku, Kyoto 606, JapanJP

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