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- Title
On L-Close Sperner Systems.
- Authors
Nagy, Dániel T.; Patkós, Balázs
- Abstract
For a set L of positive integers, a set system F ⊆ 2 [ n ] is said to be L-close Sperner, if for any pair F, G of distinct sets in F the skew distance s d (F , G) = min { | F \ G | , | G \ F | } belongs to L. We reprove an extremal result of Boros, Gurvich, and Milanič on the maximum size of L-close Sperner set systems for L = { 1 } , generalize it to | L | = 1 , and obtain slightly weaker bounds for arbitrary L. We also consider the problem when L might include 0 and reprove a theorem of Frankl, Füredi, and Pach on the size of largest set systems with all skew distances belonging to L = { 0 , 1 } .
- Subjects
EXTREMAL problems (Mathematics); INTEGERS
- Publication
Graphs & Combinatorics, 2021, Vol 37, Issue 3, p789
- ISSN
0911-0119
- Publication type
Article
- DOI
10.1007/s00373-021-02280-2