Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Three identities between Stirling numbers and the stabilizing character sequence
HTML articles powered by AMS MathViewer

by Michael Gilpin PDF
Proc. Amer. Math. Soc. 60 (1976), 360-364 Request permission

Abstract:

Let $\chi$ denote the stabilizing character of the action of the finite group G on the finite set X. Let ${\chi _k}$ denote $|G{|^{ - 1}}{\Sigma _{\sigma \in G}}\chi {(\sigma )^k}$ It is well known that ${\chi _k}$ is the number of orbits of the induced action of G on the Cartesian product ${X^{(k)}}$. We show if G is a least $(k - 1)$-fold transitive on X, then ${\chi _k}$ can be expressed in terms of Stirling numbers of both kinds. Three identities between Stirling numbers and the stabilizing character sequence are obtained.
References
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC: 05A15, 20B99
  • Retrieve articles in all journals with MSC: 05A15, 20B99
Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 60 (1976), 360-364
  • MSC: Primary 05A15; Secondary 20B99
  • DOI: https://doi.org/10.1090/S0002-9939-1976-0414376-9
  • MathSciNet review: 0414376