Affiliation: Pennsylvania State University
Email: andrews@math.psu.edu
Title Of Talk: Partitions with Short Sequences and Ramanujan's Mock Theta Functions
Abstract: In a recent paper "Integrals, Partitions and Cellular Automata" in the Transactions of the American Mathematical Society, Holroyd, Liggett and Romik evaluated an intriguing definite integral and applied it to a variety of probability models. The application to integer partitions concerned partitions in which no sequence of consecutive integers of length k appears (k=2,3,...). The authors note that in one instance, a proof of their result can also be based on a little known partition theorem of P.A. MacMahon. Our object in this talk will be to introduce these ideas and to develop the study of such partitions from a purely combinatorial, q-series point of view. Surprisingly one of Ramanujan's mysterious mock theta functions arises quite naturally.
Last update made Sat Oct 23 11:22:41 EDT 2004.
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