MathDB

Connected intersections of k subsets

Source:

January 22, 2011

floor functionceiling functioncombinatorics proposedcombinatorics

Problem Statement

Let

n

be a positive integer and

A=\{ 1,2,\ldots ,n\}

. A subset of

A

is said to be connected if it consists of one element or several consecutive elements. Determine the maximum

k

for which there exist

k

distinct subsets of

A

such that the intersection of any two of them is connected.