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How many ways are there to exchange n pennies using two(or more) types of coins?
Algebra & Discrete Mathematics| Speaker: | Prof. Sinai Robins, Temple University |
| Location: | 593 Kerr |
| Start time: | Thu, May 2 2002, 4:10PM |
Description
The coin exchange problem asks for the number of ways
we can exchange n pennies by using finitely many coins.
That is, we're given a positive integer n and positive integers a_i (the
coins) whose gcd is 1. We then ask for positive integers
x_j that solve the linear relation
n = a_1 x_1 + ... + a_d x_d.
This problem brings together many fields, and in the course of
studying this problem we uncover some
interesting new connections between combinatorics, analytic number theory
(Dedekind sums), and convex polytopes.
Today is a two-speaker session (Lipika Deka
speaks at 15:10pm).