Maximizing a combinatorial expression arising from crowd estimation
Combinatorics
2009-11-02 v1
Abstract
We determine, within 1, the value of N for which sum (s1 choose i)(s2 choose N)(s1 choose N-i)(N choose i) achieves its maximum value. Here s1 and s2 are fixed integers. This problem arises in studying the most likely value for the size of the union of A, B, and C if A and C are disjoint sets of size s1, and B is a set of size s2. Attempting to remove the 1 unit of indeterminacy leads to interesting conjectures about a family of rational functions.
Cite
@article{arxiv.0910.5725,
title = {Maximizing a combinatorial expression arising from crowd estimation},
author = {Donald M. Davis},
journal= {arXiv preprint arXiv:0910.5725},
year = {2009}
}
Comments
21 pages