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Theses/Dissertations

2017

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Articles 31 - 33 of 33

Full-Text Articles in Discrete Mathematics and Combinatorics

Pattern Containment In Circular Permutations, Charles Lanning Jan 2017

Pattern Containment In Circular Permutations, Charles Lanning

Electronic Theses and Dissertations

Pattern containment in permutations, as opposed to pattern avoidance, involves two aspects. The first is to contain every pattern at least once from a given set, known as finding superpatterns; while the second is to contain some given pattern as many times as possible, known as pattern packing. In this thesis, we explore these two questions in circular permutations and present some interesting observations. We also raise some questions and propose some directions for future study.

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Combinatorics Of Compositions, Meghann M. Gibson Jan 2017

Combinatorics Of Compositions, Meghann M. Gibson

Electronic Theses and Dissertations

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.

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Distance Magic-Type And Distance Antimagic-Type Labelings Of Graphs, Bryan Freyberg Jan 2017

Distance Magic-Type And Distance Antimagic-Type Labelings Of Graphs, Bryan Freyberg

Dissertations, Master's Theses and Master's Reports

Generally speaking, a distance magic-type labeling of a graph G of order n is a bijection f from the vertex set of the graph to the first n natural numbers or to the elements of a group of order n, with the property that the weight of each vertex is the same. The weight of a vertex x is defined as the sum (or appropriate group operation) of all the labels of vertices adjacent to x. If instead we require that all weights differ, then we refer to the labeling as a distance antimagic-type labeling. This idea can be generalized …

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