Abstract: The Statistics of Random Skew Partitions (2011 SACNAS National Conference)

Friday, October 28, 2011

Hall 1-2 (San Jose Convention Center)

Adriana Gracia , University of Texas- Pan American, Edinburg, TX

Meagan Magnoni , Rensselaer Polytechnic Institute, Troy, NY

Jesse Anderson , University of Texas- Pan American, Edinburg, TX

John Decelles , Rensselaer Polytechnic Institute, Troy, NY

Virgil Pierce, PhD , Mathematics, University of Texas- Pan American, Edinburg, TX

Gregor Kovacic , Rensselaer Polytechnic Institute, Troy , NY

We investigate plane partitions and skew partitions. In particular, we look

at processes that grow plane and skew partitions, as well as Boltzmann samplers for

plane and skew partitions. Boltzmann samplers generate matrices of nonnegative inte-

gers, which are put through Paks Bijection to create a partition. We use the generating

function for plane partitions to compare the results of these algorithms. In particular,

we investigate the statistics of plane and skew partitions, such as expected height and

expected shape for a given volume.