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Thursday, September 26, 2013

**Abstract:** Over the past several years, numerous authors have studied properties of the combinatorial objects known as overpartitions (which are natural generalizations of integer partitions). Once these new objects are defined, we will prove a number of Ramanujan-like congruences for the function which enumerates the overpartitions of weight n. We will also mention a number of restricted overpartition functions and prove arithmetic properties satisfied by these functions as well. The proof techniques will be elementary in nature, relying primarily on generating function manipulations, and the talk will be self-contained.