Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4647429 | Discrete Mathematics | 2014 | 5 Pages |
Abstract
We call a sum a1+a2+â¯+ak a partition of n of length k if a1,a2,â¦,ak and n are positive integers such that a1â¤a2â¤â¯â¤ak and n=a1+a2+â¯+ak. For i=1,2,â¦,k, we call ai the ith part of the sum a1+a2+â¯+ak. Let Pn,k be the set of all partitions of n of length k. We say that two partitions a1+a2+â¯+ak and b1+b2+â¯+bk strongly intersect if ai=bi for some i. We call a subset A of Pn,k strongly intersecting if every two partitions in A strongly intersect. Let Pn,k(1) be the set of all partitions in Pn,k whose first part is 1. We prove that if 2â¤kâ¤n, then Pn,k(1) is a largest strongly intersecting subset of Pn,k, and uniquely so if and only if kâ¥4 or k=3â¤nâ{6,7,8} or k=2â¤nâ¤3.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Peter Borg,