Mathematics Commons^™

Chutes And Ladders With Large Spinners, Darcie E. Connors, Darren B. Glass

Math Faculty Publications

We prove a conjecture from a 2011 College Mathematics Journal article addressing the expected number of turns in a Chutes and Ladders game when the spinner range is close to the length of the board. While the original paper approached the question using linear algebra and the theory of Markov processes, our main method uses combinatorics and recursion.

Reducing The Effects Of Unequal Number Of Games On Rankings, T. P. Chartier, J. Harris, K. R. Hutson, A. N. Langville, D. Martin, Charles D. Wessell

Math Faculty Publications

Ranking is an important mathematical process in a variety of contexts such as information retrieval, sports and business. Sports ranking methods can be applied both in and beyond the context of athletics. In both settings, once the concept of a game has been defined, teams (or individuals) accumulate wins, losses, and ties, which are then factored into the ranking computation. Many settings involve an unequal number of games between competitors. This paper demonstrates how to adapt two sports rankings methods, the Colley and Massey ranking methods, to settings where an unequal number of games are played between the teams. In …

Fearless Friday: Kirsten Crear, Kirsten Crear

SURGE

Even in her last semester here at Gettysburg, Kirsten Crear ’14 is fearlessly working to make changes for the future of the campus community. This semester, Kirsten introduced a STEMinists club on campus that will give female students who are STEM (an acronym for Science-Technology-Engineering-Mathematics) majors the opportunity to come together and create a community, share and discuss the difficulties they face as women in their fields of study, and support and mentor each other as they prepare to enter their fields.

Kirsten is passionate, driven, and determined, taking the initiative to bring this group of women together on campus …

Symmetric Periodic Solutions For A Class Of Differential Delay Equations With Distributed Delay, Benjamin B. Kennedy

Math Faculty Publications

We consider a nonlinear distributed delay equation where g and f are smooth, bounded, and odd and satisfy a positive and a negative feedback condition, respectively. Using elementary fixed point theory we prove the existence of a nontrivial periodic solution of period 2 + 2d satisfying certain symmetries, given certain growth conditions on f and g near zero.

A Frobenius Question Related To Actions On Curves In Characteristic P, Darren B. Glass

Math Faculty Publications

We consider which integers g can occur as the genus and of a curve defined over a field of characteristic p which admits an automorphism of degree pq, where p and q are distinct primes. This investigation leads us to consider a certain family of three-dimensional Frobenius problems and prove explicit formulas giving their solution in many cases.

Composition Of Integers With Bounded Parts, Darren B. Glass

Math Faculty Publications

In this note, we consider ordered partitions of integers such that each entry is no more than a fixed portion of the sum. We give a method for constructing all such compositions as well as both an explicit formula and a generating function describing the number of k-tuples whose entries are bounded in this way and sum to a fixed value g.