Maximizing a combinatorial expression arising from crowd estimation

Details Maximizing a combinatorial expression arising from crowd estimation Maximizing a combinatorial expression arising from crowd estimation

2009-10-29

arxiv.org/abs/0910.5725v1

Mathematics

Combinatorics

21 pages

Scientific paper

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.

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