Portland State University Discrete Mathematics Seminar

Spring 2015: Neuberger Hall 209, Mondays, 3–4pm (previous quarters)

April 13, 2015

Matthew Junge, University of Washington
The frog model on trees

On a d-ary tree, place some number (random or otherwise) of sleeping frogs at each site, as well as one awake frog at the root. Awake frogs perform simple random walk and wake any "sleepers" they encounter. A longstanding open problem: Does every frog wake up? It turns out this depends on d and the number of frogs. The proof uses two different recursions and two different versions of stochastic domination. Joint work with Christopher Hoffman and Tobias Johnson.

May 4, 2015

Ewan Kummel, Portland State University
The "100 prisoners" problem: part 2

I will (re)introduce the "100 prisoners" problem and its solution and explore more of the problem's combinatorial properties. Then I will present an unusual proof, due to Eugene Curtin and Max Warshauer, that the purported solution is in fact optimal. This talk will not presuppose the content of my previous talk on this problem.

May 11, 2015

Pieter VandenBerge, Portland State University
The "dice summing problem"

In this talk I tell you about my search for a general formula for the "dice summing problem". Given a finite set of dice with a set number of sides, how many different ways are there to roll a given sum? This search almost entirely involves techniques presented in our 300-level discrete class, elaborated appropriately. We will go over these techniques and explore the problem and solutions. I will also provide some analysis of how the exploring this problem has shaped my ideas of best practice in problem solving over the course of my first year as a Master's student.

June 1, 2015

Ronni Atchley, Portland State University
Some planar monomials in characteristic 2 and their applications

In 1968 Dembowski and Ostrom introduced planar functions over fields of odd characteristic in order to construct finite projective planes. Later it was discovered that they also have applications in cryptography, relative difference sets, and error-code correcting. Zhou introduced a definition of planar functions over fields of characteristic 2 in 2013, which, like their odd-characteristic counterparts, have various applications. We will briefly explore some planar monomials in characteristic 2 and their application in the construction of finite projective planes via relative difference sets.

Special place and time:
Neuberger Hall 373, Wednesday, June 3, 2015, 4pm

Joseph Wooster, Portland State University
Elements of large order in class groups of imaginary quadratic fields

For any prime p such that p ≡ 3 (mod 4), we will describe an infinite family of imaginary quadratic fields whose ideal class groups contain an element of order p. We will compare this result with the Cohen-Lenstra heuristics, which assert that a positive proportion of such fields have ideal class groups divisible by p.