Discrete Mathematics and Combinatorics Commons^™

Distribution Of Permutation Statistics Across Pattern Avoidance Classes, And The Search For A Denert-Associated Condition Equivalent To Pattern Avoidance, Joshua Thomas Agustin Davies

Dissertations, Master's Theses and Master's Reports

We begin with a discussion of the symmetricity of $\maj$ over $\des$ in pattern avoidance classes, and its relationship to $\maj$-Wilf equivalence. From this, we explore the distribution of permutation statistics across pattern avoidance for patterns of length 3 and 4.

We then begin discussion of Han's bijection, a bijection on permutations which sends the major index to Denert's statistic and the descent number to the (strong) excedance number. We show the existence of several infinite families of fixed points for Han's bijection.

Finally, we discuss the image of pattern avoidance classes under Han's bijection, for the purpose of finding …

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 …