Extremal set systems with weakly restricted intersections
type: Item
instance of: scholarly article
title: Extremal set systems with weakly restricted intersections
zbMATH Open document ID: 0985.05051
published in: Combinatorica
publication date: 2000-05-14T00:00:00Z
review text: In this excellent paper extremal set systems with intersections of restricted cardinality are studied. If, say, each intersection has even cardinality then a linear algebraic tool (linear independence of the characteristic vectors of the subsets) gives an upper bound for the number of subsets. If, for each \(i\), the cardinality constraints for \(A_i \cap A_j\) can be violated by at most \(s\) subsets of form \(A_j\) then this ``\(s\)-weak version'' of the problem can still be handled by additional tools (from extremal graph theory, for instance) if \(s\) is relatively small. The author gives a tight upper bound for the weak version of the ``odd town'' problem (odd subsets with even intersections); for the weak version of the non-uniform Fisher inequality (leading to a new, extremal set theoretic characterization of Hadamard's matrices); and for the weak version of the ``even town'' problem (even intersections only). This latter leads to results in case of restricted multi-intersections as well.
reviewed by: András Recski
Mathematics Subject Classification ID: 05D05
Mathematics Subject Classification ID: 05B20
zbMATH DE Number: 1446813
zbMATH Keywords: restricted intersections
zbMATH Keywords: extremal sets
author: Van Vu
MaRDI profile type: Publication
full work available at URL: s004939970008
OpenAlex ID: W1968335839
DOI: 10.1007/S004939970008
description: scientific article; zbMATH DE number 1446813