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Analysis of the Generalized Catalan Orbits

Mott, Brittany Nicole
http://rave.ohiolink.edu/etdc/view?acc_num=akron1302396750

Abstract Details

2011, Master of Science, University of Akron, Mathematics.
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.
James Cossey, Dr. (Advisor)
102 p.
Mathematics
Catalan Numbers; Generalized Catalan Numbers; Burnside's Lemma; Orbits; Dissection of polygons

Recommended Citations

Citations

  • Mott, B. N. (2011). Analysis of the Generalized Catalan Orbits [Master's thesis, University of Akron]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=akron1302396750

    APA Style (7th edition)

  • Mott, Brittany. Analysis of the Generalized Catalan Orbits. 2011. University of Akron, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=akron1302396750.

    MLA Style (8th edition)

  • Mott, Brittany. "Analysis of the Generalized Catalan Orbits." Master's thesis, University of Akron, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=akron1302396750

    Chicago Manual of Style (17th edition)

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© 2011, all rights reserved.
This open access ETD is published by University of Akron and OhioLINK.