Undergraduate Seminar: "Number of steps of the Hillman-Grassl algorithm for partitions of stretched staircase shape"
Abstract: We define stretched staircase shapes to be integer partitions with such that the difference between two consecutive parts is m, and the smallest part is 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 has a nice factorization into linear terms.
Host: Adeli Hutton