PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Matthew Katz, James Sellers, Stephanie Zerby, George Andrews.

Title:Congruences modulo 4 for broken k-diamond partitions
Seminar:Combinatorics/Partitions Seminar
Speaker:Ernest X. W. Xia, Jiangsu University
Abstract:
The notion of broken k-diamond partitions was introduced by Andrews and Paule. Let ∆_k(n) denote the number of broken k-diamond partitions of n for a fixed positive integer k. Recently, a number of parity results satisfied by ∆_k(n) for small values of k have been proved by Radu and Sellers and so on. However, congruences modulo 4 for ∆_k(n) are unknown. In this paper, we will prove five congruences modulo 4 for ∆_5(n), four infinite families of congruences modulo 4 for ∆_7(n) and one congruence modulo 4 for ∆_11(n) by employing theta function identities. Furthermore, we will prove a new parity result for ∆_2(n).

Room Reservation Information

Room Number:MB106
Date:04 / 19 / 2016
Time:11:15am - 12:05pm