Senior Honors Thesis Presentation: "The number of steps of the Hillman Grassl algorithm for plane partitions of bounded height and certain shapes."

Abstract: We define stretched staircase shapes to be integer partitions $\lambda = (mn, m(n-1),\ldots, 2m,m)$. The case $m=1$ gives the standard staircase shape partitions. We analyze the generating function of the number of steps the Hillman-Grassl algorithm takes to finish on the set of semistandard young tableaux of stretched staircase shape with bounded entries. We show that this has the generating function is $(1+mt)^{\binom{n+1}{2}}$. We then analyze this generating function on other arbitrary shapes.

Host: John Shareshian