Analysis of the Generalized Catalan Orbits

Analysis of the Generalized Catalan Orbits

Bibliographic Details
Main Author: Mott, Brittany Nicole
Language:English
Published: University of Akron / OhioLINK 2011
Subjects:
Mathematics
Catalan Numbers
Generalized Catalan Numbers
Burnside's Lemma
Orbits
Dissection of polygons
Online Access:http://rave.ohiolink.edu/etdc/view?acc_num=akron1302396750
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spelling ndltd-OhioLink-oai-etd.ohiolink.edu-akron13023967502021-08-03T05:26:32Z Analysis of the Generalized Catalan Orbits Mott, Brittany Nicole Mathematics Catalan Numbers Generalized Catalan Numbers Burnside's Lemma Orbits Dissection of polygons The Catalan numbers are well-known in the field of combinatorics. This sequence of integers counts a variety of combinatorial objects including binary trees, triangulations of regular polygons, and paths on a square grid which lie below the diagonal. Of the hundreds of realizations of the Catalan numbers, the majority can be extended and considered under the scope of the generalized Catalan numbers. The generalized Catalan numbers consider a second parameter in addition to the single parameter of the regular Catalan numbers, consequently forming a grid of values instead of a single sequence of integers. Although a formula has been developed to determine the generalized Catalan number when given values for the two parameters, much is still unknown about the generalized Catalan numbers. This thesis will count the generalized Catalan orbits, defined to be the orbits of the combinatorial objects counted by the generalized Catalan numbers. Two realizations of the generalized Catalan numbers, p-ary trees and the dissection of regular polygons, will be used throughout our study of the generalized Catalan orbits. A variety of techniques will be used to create formulas which describe the number of generalized Catalan orbits in terms of the given parameters. 2011-05-16 English text University of Akron / OhioLINK http://rave.ohiolink.edu/etdc/view?acc_num=akron1302396750 http://rave.ohiolink.edu/etdc/view?acc_num=akron1302396750 unrestricted This thesis or dissertation is protected by copyright: all rights reserved. It may not be copied or redistributed beyond the terms of applicable copyright laws.
collection NDLTD
language English
sources NDLTD
topic Mathematics
Catalan Numbers
Generalized Catalan Numbers
Burnside's Lemma
Orbits
Dissection of polygons
spellingShingle Mathematics
Catalan Numbers
Generalized Catalan Numbers
Burnside's Lemma
Orbits
Dissection of polygons
Mott, Brittany Nicole
Analysis of the Generalized Catalan Orbits
author Mott, Brittany Nicole
author_facet Mott, Brittany Nicole
author_sort Mott, Brittany Nicole
title Analysis of the Generalized Catalan Orbits
title_short Analysis of the Generalized Catalan Orbits
title_full Analysis of the Generalized Catalan Orbits
title_fullStr Analysis of the Generalized Catalan Orbits
title_full_unstemmed Analysis of the Generalized Catalan Orbits
title_sort analysis of the generalized catalan orbits
publisher University of Akron / OhioLINK
publishDate 2011
url http://rave.ohiolink.edu/etdc/view?acc_num=akron1302396750
work_keys_str_mv AT mottbrittanynicole analysisofthegeneralizedcatalanorbits
_version_ 1719420138935025664

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