We consider the random poset P(n, p) which is generated by first selecting each subset of [n]=[1, ..., n] with probability p and then ordering the selected subsets by inclusion. We give asymptotic estimates of the size of the maximum antichain for arbitrary p= p(n). In particular, we prove that if p
A Family of Inequalities for Intersecting Antichain of Subsets of an n-set
β Scribed by Changyu Wang; Huishan Zhou
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 252 KB
- Volume
- 17
- Category
- Article
- ISSN
- 0195-6698
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Erdos and Rado defined a A-system, as a family in which every two members have the same intersection. Here we obtain a new upper bound on the maximum cardinality q ( n , q ) of an n-uniform family not containing any A-system of cardinality q. Namely, we prove that, for any a > 1 and q , there exists
The intersection radius of a finite collection of geometrical objects in the plane is the radius of the smallest closed disk that intersects all the objects in the collection. Bhattacharya et al. showed how the intersection radius can be found in linear time for a collection of line segments in the
ry gywwxsgesyx eww Γ F ngewF wthF wehF UV @IWWVA TD RPUΒ± Β±RQH rungD xFEjF e xew wethod for glss of xonliner etEvlued ritionl snequlities sn this pper we onstrut new itertive lgorithm for solving new lss of nonliner vritionl inequlities with setE vlued mppingD nd give some onvergene nlysis of itertiv
Let be a finite subset of the Cartesian product W 1 Γ β’ β’ β’ Γ W n of n sets. For A β {1, 2, . . . , n}, denote by A the projection of onto the Cartesian product of W i , i β A. Generalizing an inequality given in an article by Shen, we prove that , 2, . . . , n}. This inequality is applied to give s
Let 7 be an unknown covariance matrix. Perturbation (in)equalities are derived for various scale-invariant functionals of 7 such as correlations (including partial, multiple and canonical correlations) or angles between eigenspaces. These results show that a particular confidence set for 7 is canoni