For more information about this meeting, contact Robert Vaughan.
|Title:||Parity Results for Broken k-Diamond Partitions and (2k+1)-Cores|
|Seminar:||Algebra and Number Theory Seminar|
|Speaker:||James Sellers, Penn State University|
|In 2007, George Andrews and Peter Paule introduced broken k-diamond partitions as part of their work involving MacMahon's partition analysis. In that paper, they proved one congruence modulo 3 for broken 1-diamond partitions and conjectured a few other congruences modulo 2 for certain families of broken k-diamond partitions. Subsequently, Hirschhorn and Sellers provided a new proof of the modulo 3 congruence mentioned above as well as elementary proofs of a number of congruences modulo 2 for broken k-diamond partitions. In this talk, we present a much more extensive list of parity results for broken k-diamond partitions, and we show that these results are intimately related to new parity results for (2k+1)-cores. Indeed, for each prime t, 5 <= t <= 23, we explicitly demonstrate (t-1)/2 different Ramanujan-like congruences modulo 2 for t-cores. This is joint work with Silviu Radu, RISC, Johannes Kepler University, Austria.|
Room Reservation Information
|Date:||04 / 22 / 2010|
|Time:||11:15am - 12:05pm|