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Speaker: Selcuk Aygin

Date: Friday, October 11

Time: 12 to12:50 p.m.

Location: C640

Title:

Ramanujan's congruences for the partition function, ranks and cranks

Abstract:

Let n be a natural number and p(n) denote the partition function, the number of different ways to write n as a sum of a collection of smaller numbers. Ramanujan has proven the following elementary congruences for the partition function:

p(5n+4) = 0 mod 5

p(7n+5) = 0 mod 7

p(11n+6) = 0 mod 11

In this talk we prove the first two of the above congruences using analytic techniques. We then introduce ranks and cranks which give combinatorial interpretations for these congruences. Finally, we will introduce some open problems in the study of partition functions, ranks and cranks.

#### Contact:

Barb Hodgson | hodgsonb@uleth.ca | (403) 329-2470 | http://www.uleth.ca/artsci/math-computer-science