Intro
Preface I
Preface II
Contents
Ratio Balancing Numbers
1 Introduction
2 Ratio Balancing Numbers and Related Quantities
3 Counting Ratio Balancing Numbers
4 Functions Generating Ratio Balancing Numbers and Related Results
4.1 One Jump Case
4.2 Two Jump Case
References
An Unexpected Digit Permutation from Multiplying in Any Number Base
1 Introduction
2 Main Theorem
3 Other Interesting Results
4 Demonstration of Results
5 Questions for Further Investigation
References
A & Z Sequences for Double Riordan Arrays
1 Introduction

2 Double Riordan: A & Z Sequences
3 New Subgroups
4 Conclusion
References
Constructing Clifford Algebras for Windmill and Dutch Windmill Graphs
A New Proof of the Friendship Theorem
1 Introduction
2 Preliminaries for a Clifford Graph Algebra
3 Clifford Algebras for Windmill and Dutch Windmill Graphs
3.1 Windmill Graphs
3.2 Dutch Windmill Graphs
3.3 The Friendship Graph
3.4 The Clifford Algebra for the Friendship Graph
3.5 The Clifford Algebra for the Class of Windmill Graphs
3.6 The Clifford Algebra for the Class of Dutch Windmill Graphs

4 The Friendship Theorem
4.1 Standard Preliminaries for the Friendship Theorem
4.2 Clifford Algebra Preliminaries for the Friendship Theorem
4.3 Proof of the Friendship Theorem
5 Concluding Remarks
References
Finding Exact Values of a Character Sum
1 Introduction
2 Proofs
3 Counting Points on left parenthesis asterisk asterisk asterisk right parenthesis(***)
4 Examples
5 Conclusion
References
On Minimum Index Stanton 44-Cycle Designs
1 Introduction
2 Stanton 4-Cycles
3 Small Decompositions
4 Decompositions via Graph Labellings
5 Main Result

1 Introduction
2 Main Results
References
On Rainbow Mean Colorings of Trees
1 Introduction
2 Rainbow Mean Colorings
3 The Rainbow Mean Index of Trees
4 Cubic Caterpillars
5 Subdivided Stars
6 Double Stars
References
Examples of Edge Critical Graphs in Peg Solitaire
1 Introduction
2 The Hairy Complete Bipartite Graph
3 Edge Critical Results
4 Graphs on Eight Vertices
References
Regular Tournaments with Minimum Split Domination Number and Cycle Extendability
1 The Lower Bound
2 Properties of Tournaments That Meet the Bound
References