An investigation on partitions with equal products
Abstract
An ordered triple (s,p,n) is called admissible if there exist two different multisets X={x1,x2,…,xn} and Y={y1,y2,…,yn} such that X and Y share the same sum s, the same product p, and the same size n. We first count the number of n such that (s,p,n) are admissible for a fixed s. We also fully characterize the values p such that (s,p,n) is admissible. Finally, we consider the situation where r different multisets are needed, instead of just two. This project is also related to John Conway’s wizard puzzle from the 1960s.
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