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Stable Kneser hypergraphs and ideals in  with the Nikodým property
Author(s):
Noga
Alon;
Lech
Drewnowski;
Tomasz
Łuczak
Journal:
Proc. Amer. Math. Soc.
137
(2009),
467-471.
MSC (2000):
Primary 05A17, 05C15, 11B05
Posted:
August 19, 2008
MathSciNet review:
2448565
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Abstract:
We use stable Kneser hypergraphs to construct ideals in  which are not nonatomic yet have the Nikodým property.
References:
-
- 1.
- N. Alon, P. Frankl and L. Lovász, The chromatic number of Kneser hypergraphs, Trans. Amer. Math. Soc. 298 (1986), 359-370. MR 857448 (88g:05098)
- 2.
- H. Auerbach, Über die Vorzeichenverteilung in unendlichen Reihen, Studia Math. 2 (1930), 228-230.
- 3.
- L. Drewnowski and I. Labuda, Vector series whose lacunary subseries converge, Studia Math. 138 (2000), 53-80. MR 1750322 (2001e:40004)
- 4.
- L. Drewnowski and P.J. Paúl, The Nikodým property for ideals of sets defined by matrix summability methods, Rev. R. Acad. Cienc. Exact. Fis. Nat. (Esp) 94 (2000), 485-503. MR 1865750 (2002i:46002)
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- J. Matoušek, Using the Borsuk-Ulam theorem. Lectures on topological methods in combinatorics and geometry, Springer-Verlag, Berlin, 2003. MR 1988723 (2004i:55001)
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- A. Schrijver, Vertex-critical subgraphs of Kneser graphs, Nieuw Arch. Wisk. (3) 26 (1978), no. 3, 454-461. MR 512648 (80g:05037)
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Additional Information:
Noga
Alon
Affiliation:
Schools of Mathematics and Computer Science, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel - and - Institute for Advanced Study, Princeton, New Jersey 08540
Email:
nogaa@tau.ac.il
Lech
Drewnowski
Affiliation:
Faculty of Mathematics and Computer Science, A.~ Mickiewicz University, Umultowska 87, 61-614 Poznan, Poland
Email:
drewlech@amu.edu.pl
Tomasz
Łuczak
Affiliation:
Faculty of Mathematics and Computer Science, A.~ Mickiewicz University, Umultowska 87, 61-614 Poznan, Poland
Email:
tomasz@amu.edu.pl
DOI:
10.1090/S0002-9939-08-09588-9
PII:
S 0002-9939(08)09588-9
Keywords:
Kneser graph,
divergent series,
chromatic number,
Nikod\'ym property
Received by editor(s):
January 22, 2008
Posted:
August 19, 2008
Additional Notes:
The first author is supported by the Israel Science Foundation, by a USA-Israeli BSF grant, by the Hermann Minkowski Minerva Center for Geometry at Tel Aviv University, and by the Von~Neumann Fund
The third author is supported by the Foundation for Polish Science
Communicated by:
Jim Haglund
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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