A Gessel-Viennot-Type Method for Cycle Systems
Chris Hanusa
University of Washington
In the 1980's, Gessel and Viennot presented a determinantal
method for counting non-intersecting lattice paths. We present an
extension of this method to counting non-intersecting cycle systems in a
particular type of graph we call a hamburger. This ``Hamburger
Theorem'' gives a purely combinatorial proof of a determinantal formula
for the number of domino tilings of an Aztec diamond, as first introduced
by Brualdi and Kirkland in 2003. We present this argument and expand upon
the Hamburger Theorem's applications to domino tilings of other regions
of interest.