Term of Award
Spring 2017
Degree Name
Master of Science in Mathematics (M.S.)
Document Type and Release Option
Thesis (open access)
Copyright Statement / License for Reuse
This work is licensed under a Creative Commons Attribution 4.0 License.
Department
Department of Mathematical Sciences
Committee Chair
Hua Wang
Committee Member 1
Daniel Gray
Committee Member 2
Andrew Sills
Committee Member 3
David Stone
Abstract
Integer compositions and related enumeration problems have been extensively studied. The cyclic analogues of such questions, however, have significantly fewer results. In this thesis, we follow the cyclic construction of Flajolet and Soria to obtain generating functions for cyclic compositions and n-color cyclic compositions with various restrictions. With these generating functions we present some statistics and asymptotic formulas for the number of compositions and parts in such compositions. Combinatorial explanations are also provided for many of the enumerative observations presented.
Recommended Citation
M.M. Gibson, Combinatorics of Compositions, \textit{Electronic Theses & Dissertations}, (2017).
Research Data and Supplementary Material
No
