Degree Type

Dissertation

Date of Award

2002

Degree Name

Doctor of Philosophy

Department

Mathematics

First Advisor

Jonathan D. H. Smith

Abstract

Let (Q, G) be a permutation representation. The restricted diagonal action of G on the subset of Qn containing n-tuples in which no elements appear more than m times, the so-called multi-restricted power of permutation representation with restriction m, is studied. The orbit decompositions of these actions involve a new class of numbers, the so-called multi-restricted numbers of the first and second kinds with restriction m. The multi-restricted numbers of the second kind without a restriction are the Stirling numbers of the second kind, and the multi-restricted numbers of the second kind with restriction 2 are reparametrized coefficients of Bessel polynomials, the so-called Bessel numbers. The multi-restricted numbers of the second kind with the restriction m ≥ 3 are entirely new, and this thesis is devoted to a study of this new series of numbers.

DOI

https://doi.org/10.31274/rtd-180813-11329

Publisher

Digital Repository @ Iowa State University, http://lib.dr.iastate.edu

Copyright Owner

Ji Young Choi

Language

en

Proquest ID

AAI3051454

File Format

application/pdf

File Size

58 pages

Included in

Mathematics Commons

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