The combination of the fields of probability and combinatorics is currently an object of much research. However, not many undergraduates or lay people have the opportunity to see how these areas can work together. We present what we hope is an accessible introduction to the possibilities easily available to many more people through the use of many examples and understandable explanations. We introduce topics of generating functions and tree structures formed through both independent strings and suffixes, as well as how we can find correlation polynomials, expected values, second moments, and variances of the number of nodes in a tree using indicator functions. Then we show a higher order example that includes matrices as the basis for its generating functions. The study of this unique field has many applications in areas including data compression, computational biology with the human genome, and computer science with binary strings.
Mark Daniel Ward, Department of Statistics, Purdue University
Sutton, Deborah and Wong, Booi Yee
"Exploring String Patterns with Trees,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 12
, Article 11.
Available at: http://scholar.rose-hulman.edu/rhumj/vol12/iss2/11