Apr. 3: Alex Burstein: Dumont permutations of the third kind

We consider a new set of permutations that we prove is equinumerous to Dumont permutations of the first and second kinds, as well as to the so-called surjective pistols. We also find a pair of statistics on Dumont permutations of the first and third kind that yield the Seidel triangle for Genocchi numbers.

Mar. 27: Dan Cranston, U. of Illinois at Urbana-Champaign: Coloring and List-coloring of Graphs

We begin by defining graph coloring and list-coloring. In the first half of the talk, we prove well-known results, such as the 5-choosability of planar graphs and the unbounded choice number of bipartite graphs. In the second half of the talk, we present a number of our own results; we include topics such as list edge-coloring planar graphs, list coloring squares of subcubic graphs, and strong edge-coloring graphs with maximum degree 4. We also introduce the discharging method, which we use in three of our results.

(Fri.) Mar. 23: Jason Grout, Bringham Young University: The minimum rank problem over the finite field of order 2: minimum rank 3

We consider all symmetric n-by-n matrices with a fixed off-diagonal zero/nonzero pattern Z. The minimum rank for the pattern Z is the minimum rank of all such matrices. It is known that, for each rank k between the minimum rank of Z and n, there are symmetric matrices having the zero/nonzero pattern Z and rank k.

Determining the minimum rank of a pattern is then the important but difficult question. Working with matrices over a finite field simplifies and gives insight into the problem over an infinite field. I will give a report on recent results with Wayne Barrett and Raphael Loewy in classifying and recognizing the zero/nonzero patterns having minimum rank less than or equal to 3 in the finite field of order 2. I will describe how some of our results extend to determining the minimum rank of patterns of matrices over infinite fields. I will also demonstrate an online graph database that I developed which helped in the investigation of the problem.

Feb. 20: Jeremy Alm and Jake Manske: A probabilistic nightmare: Constructing the world's worst graph (sort of)

We will discuss the the special case of the flexible atom conjecture we proved back at the EXCILL conference at UIUC in November.

Feb. 6: Ryan Martin: Beauty is rare: The Hoffman-Singleton theorem

Let G be a graph which is d-regular, has diameter 2 and has no 3-cycles or 4-cycles.  For what values of d is this possible?

The Hoffman-Singleton theorem gives that this set of values is {2,3,7,57} -- but maybe not 57.  The elegant and surprising proof is an application of elementary linear algebraic facts. 

This talk is a brief introduction to the concept of positional games and highlights the classic theorem of Erdõs and Selfridge.

This talk is a recent result in the area of positional games and is the first example, to our knowledge, of an uncontrived game in which probabilistic intuition can fail entirely and the behavior of the game changes drastically even when the game is fair.
This is joint work with József Balogh and András Pluhár.   

ISU Discrete Math speakers at the AMS Central Sectional Meeting:

• Maria Axenovich in Graph Theory Special Session
• Gargi Bhattacharyya in Association Schemes and Related Topics Special Session
• Luz DeAlba (Drake University) in Combinatorial Matrix Theory Special Session
• Leslie Hogben in Combinatorial Matrix Theory Special Session
• Joohyung Kim in Association Schemes and Related Topics Special Session
• Y. T. Poon in Combinatorial Matrix Theory Special Session
• Jonathan D. H. Smith in Association Schemes and Related Topics Special Session
• Sung-Yell Song in Association Schemes and Related Topics Special Session
• Amy Wangsness (Fitchburg State College) in Combinatorial Matrix Theory Special Session