Let ${\cal F}$ be a set of blocks of a $t$-set $X$. A pair $(X,{\cal F})$ is called an $(w,r)$-cover-free family ($(w,r)-$CFF) provided that, the intersection of any $w$ blocks in ${\cal F}$ is not contained in the union of any other $r$ blocks in ${\cal F}$.We give new asymptotic lower bounds for the number of minimum points $t$ in a $(w,r)$-CFF when $w\le r=|{\cal F}|^\epsilon$ for some constant $\epsilon\ge 1/2$.
@article{10_37236_5202,
author = {Ali Z. Abdi and Nader H. Bshouty},
title = {Lower bounds for cover-free families},
journal = {The electronic journal of combinatorics},
year = {2016},
volume = {23},
number = {2},
doi = {10.37236/5202},
zbl = {1339.05030},
url = {http://geodesic.mathdoc.fr/articles/10.37236/5202/}
}
TY - JOUR
AU - Ali Z. Abdi
AU - Nader H. Bshouty
TI - Lower bounds for cover-free families
JO - The electronic journal of combinatorics
PY - 2016
VL - 23
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/5202/
DO - 10.37236/5202
ID - 10_37236_5202
ER -
%0 Journal Article
%A Ali Z. Abdi
%A Nader H. Bshouty
%T Lower bounds for cover-free families
%J The electronic journal of combinatorics
%D 2016
%V 23
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/5202/
%R 10.37236/5202
%F 10_37236_5202
Ali Z. Abdi; Nader H. Bshouty. Lower bounds for cover-free families. The electronic journal of combinatorics, Tome 23 (2016) no. 2. doi: 10.37236/5202
