Three identities between Stirling numbers and the stabilizing character sequence
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- 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
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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