Byungchan KimAffiliation: University of Illinois, Urbana Email: bkim4@illinois.edu Title Of Talk: Combinatorics of partial theta functions Abstract: A partial theta function is a sum of the form $\sum_{n=0}^{\infty} (-1)^{n}q^{n(n-1)/2}x^{n}$. Combinatorially, identities containing partial theta function are very interesting since they indicate what remains after numerous cancellations of certain kinds of partitions. In this talk, we will discuss the combinatorics of some identities involving partial theta functions in Ramanujan's lost notebook. After this, we define a subpartition of a partition, which is a generalization of the Rogers-Ramanujan subpartition that was introduced by L. Kolitsch. Finally, we will see how subpartitions are related to partial theta functions.
Last update made Fri Feb 27 20:03:43 EST 2009.
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