Multi-restricted numbers and powers of permutation representations

Date
2002-01-01
Authors
Choi, Ji Young
Major Professor
Advisor
Jonathan D. H. Smith
Committee Member
Journal Title
Journal ISSN
Volume Title
Publisher
Altmetrics
Authors
Research Projects
Organizational Units
Mathematics
Organizational Unit
Journal Issue
Series
Department
Mathematics
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.

Comments
Description
Keywords
Citation
Source