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.

Author Bio

Deborah Sutton graduated from Purdue University with a degree in Actuarial Science and Statistics in May 2011. She hopes to pursue a career in math education and is excited to see what adventures the next stage in life will bring. In her spare time, she enjoys spending time with her family and friends, playing piano and singing, and taking long walks outside.

Booi Yee Wong is an actuarial science and statistics undergraduate student at Purdue University. She is currently pursuing Purdue actuarial science honors program and ASA (Associate of the Society Actuaries) designation . After completing her studies, she wishes to become an actuary specializing in health insurance. She enjoys cycling, traveling, and collecting pins.