Name
Abstract | ||
|---|---|---|
The trace of a set F on a another set X is F vertical bar(X) = F boolean AND X and the trace of a family F of sets on X is F(X) = {F vertical bar(X) : F is an element of F}. In this note we prove that if a k-uniform family F subset of (([n])(k)) has the property that for any k-subset X the trace F vertical bar(X) does not contain a maximal chain (a family C(0) subset of C(1) subset of ... subset of C(k) with vertical bar C(i)vertical bar = i), then vertical bar F vertical bar <= ((n-1)(k-1)). This bound is sharp as shown by {F is an element of (([n])(k)), 1 is an element of F}. Our proof gives also the stability of the external family. |
Year | Venue | Field |
|---|---|---|
2009 | ELECTRONIC JOURNAL OF COMBINATORICS | Discrete mathematics,Combinatorics,Mathematics |
DocType | Volume | Issue |
Journal | 16.0 | 1.0 |
ISSN | Citations | PageRank |
1077-8926 | 3 | 0.55 |
References | Authors | |
6 | 1 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Balázs Patkós | 1 | 85 | 21.60 |