International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1982 / Article

Open Access

Volume 5 |Article ID 305381 | https://doi.org/10.1155/S0161171282000696

Chong-Yun Chao, Caroline I. Deisher, "Equivalence classes of functions on finite sets", International Journal of Mathematics and Mathematical Sciences, vol. 5, Article ID 305381, 18 pages, 1982. https://doi.org/10.1155/S0161171282000696

Equivalence classes of functions on finite sets

Revised07 Jun 1982

Abstract

By using Pólya's theorem of enumeration and de Bruijn's generalization of Pólya's theorem, we obtain the numbers of various weak equivalence classes of functions in RD relative to permutation groups G and H where RD is the set of all functions from a finite set D to a finite set R, G acts on D and H acts on R. We present an algorithm for obtaining the equivalence classes of functions counted in de Bruijn's theorem, i.e., to determine which functions belong to the same equivalence class. We also use our algorithm to construct the family of non-isomorphic fm-graphs relative to a given group.

Copyright © 1982 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


More related articles

 PDF Download Citation Citation
 Order printed copiesOrder
Views102
Downloads371
Citations

We are committed to sharing findings related to COVID-19 as quickly as possible. We will be providing unlimited waivers of publication charges for accepted research articles as well as case reports and case series related to COVID-19. Review articles are excluded from this waiver policy. Sign up here as a reviewer to help fast-track new submissions.