Colby Lamb, University of Nebraska - Lincoln
Colby Lamb
University of Nebraska - Lincoln
Alternating Sign Matrices and Domino Tiling of the Aztec Diamond
First, we will look at the definition of an alternating matrix (AMS) and the Alternating matrix conjecture. Then we will look at its correspondence to monotone triangles and square ice. These are among some of the correspondences used in some of the proofs to the alternating sign matrices conjecture. We will then look at the Aztec Diamonds and the number of different ways to tile with dominos an Aztec Diamond. To calculate the number of tilings we first must define a height function for the tiling of size n, then show the correspondence to two alternating matrices of size n and n + 1. If there is time, we will then go on to prove the number of different domino tilings of an Aztec Diamond of size n.
Feel free to share!
