Thursday, November 15, 2018
Time  Items 

All day 

3pm 
11/15/2018  3:00pm To play the dollar game on a graph, start by assigning to each vertex a number of dollars of either wealth or debt. From this initial state, called a divisor, the vertices lend and borrow with their neighbors according to chipfiring rules in an attempt to reach a debtfree state. The set of all possible winning states is the complete linear system of the divisor. We are interested in determining its cardinality. In the figure below, each vertex represents one of the 201 winning positions resultingfrom giving ten dollars to one vertex of the cycle graph on five vertices. This is joint work with Sarah Brauner and Forrest Glebe. Location:
LOM 202

4pm 
11/15/2018  4:00pm Let Q_d be the ddimensional Hamming cube (hypercube) and N=2^d. We discuss the number of proper (vertex) colorings of Q_d given q colors. It is easy to see that there are exactly 2 proper 2colorings, but for q>2, the number of qcolorings of Q_d is highly nontrivial. Since Galvin (2002) proved that the number of 3colorings is asymptotically 6e2^{N/2}, the other cases remained open so far. In this talk, we prove that the number of 4colorings of $Q_d$ is asymptotically 6e2^N, as was conjectured by Engbers and Location: 