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Chicken nuggets and the Frobenius number

Tuesday, November 1, O'Connor 106

Speaker: Cornelia Van Cott, University of San Francisco

Title: Chicken nuggets and the Frobenius number

Abstract: Suppose chicken nuggets are sold in packages of size 6, 9, and 20. With these package sizes, if you wanted to order, say, 25 chicken nuggets, you would be out of luck. After some investigation, one will discover many different sizes which also cannot be ordered; the largest such size is 43.  You cannot order 43 nuggets, but you can order N chicken nuggets for all N>43, given the package sizes of 6, 9, and 20. This problem, the so-called Chicken Nugget Problem, is a special case of a classical question first investigated by Frobenius and Sylvester in the nineteenth century. The more general question goes as follows: given a finite set A of positive integers, what is the largest number which cannot be written as a nonnegative integral linear combination of elements in A? This number, denoted g(A), is called the Frobenius number of A. We will discuss the special case where A contains only two integers. We will also consider related results, including Sylvester's Theorem which counts the integers that cannot be represented as combinations of integers in A.
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