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d-Galvin families
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0002-5379-345X
Univ Bordeaux, LaBRI, Bordeaux, France..
KTH, School of Electrical Engineering and Computer Science (EECS).
2020 (English)In: The Electronic Journal of Combinatorics, ISSN 1097-1440, E-ISSN 1077-8926, Vol. 27, no 1, article id P1.36Article in journal (Refereed) Published
Abstract [en]

The Galvin problem asks for the minimum size of a family F subset of ([n]n/2) with the property that, for any set A of size n/2, there is a set S is an element of F which is balanced on A, meaning that vertical bar S boolean AND A vertical bar = vertical bar S boolean AND ( A) over bar vertical bar. We consider a generalization of this question that comes from a possible approach in complexity theory. In the generalization the required property is, for any A, to be able to find d sets from a family F subset of ([n]n/d) that form a partition of [n] and such that each part is balanced on A. We construct such families of size polynomial in the parameters n and d.

Place, publisher, year, edition, pages
ELECTRONIC JOURNAL OF COMBINATORICS , 2020. Vol. 27, no 1, article id P1.36
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-269463DOI: 10.37236/8432ISI: 000513911100005Scopus ID: 2-s2.0-85079448290OAI: oai:DiVA.org:kth-269463DiVA, id: diva2:1413335
Note

QC 20200310

Available from: 2020-03-10 Created: 2020-03-10 Last updated: 2020-05-11Bibliographically approved

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Håstad, Johan

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