Paper Info
Title
Profile polytopes of some classes of families.
Abstract
The profile vector of a family F of subsets of an n-element set is (f (0),f (1),aEuro broken vertical bar,f (n) ) where f (i) denotes the number of the i-element members of F. The extreme points of the set of profile vectors for some class of families has long been studied. In this paper we introduce the notion of k-antichainpair families and determine the extreme points of the set of profile vectors of these families, extending results of Engel and P.L. ErdAs regarding extreme points of the set of profile vectors of intersecting, co-intersecting Sperner families. Using this result we determine the extreme points of the set of profile vectors for some other classes of families, including complement-free k-Sperner families and self-complementary k-Sperner families. We determine the maximum cardinality of intersecting k-Sperner families, generalizing a classical result of Milner from k = 1.
Year
DOI
Venue
2013
10.1007/s00493-013-2917-y
Combinatorica
Field
DocType
Volume
Extreme point,Discrete mathematics,Combinatorics,Generalization,Cardinality,Polytope,Mathematics
Journal
33
Issue
ISSN
Citations 
2
0209-9683
1
PageRank 
References 
Authors
0.40
6
1
Name
Order
Citations
PageRank
Dániel Gerbner14621.61