Hostname: page-component-745bb68f8f-d8cs5 Total loading time: 0 Render date: 2025-02-11T02:02:31.498Z Has data issue: false hasContentIssue false

All Maximum Size Two-Part Sperner Systems: In Short

Published online by Cambridge University Press:  01 July 2007

HAROUT AYDINIAN
Affiliation:
Department of Mathematics, University of Bielefeld, PO Box 100131, D-33501, Bielefeld, Germany (e-mail: ayd@uni-bielefeld.de)
PÉTER L. ERDŐS
Affiliation:
A. Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, PO Box 127, H-1364Hungary (e-mail: elp@renyi.hu)
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this note we give a very short proof for the description of all maximum size two-part Sperner systems.

Type
Paper
Copyright
Copyright © Cambridge University Press 2007

References

[1]Erdős, Paul (1945) On a lemma of Littlewood and Offord. Bull. Amer. Math. Soc. 51 898902.CrossRefGoogle Scholar
[2]Erdős, P. L. and Katona, G. O. H. (1986) Convex hulls of more-part Sperner families. Graphs Combin. 2 123134.CrossRefGoogle Scholar
[3]Erdős, P. L. and Katona, G. O. H. (1986) All maximum 2-part Sperner families. J. Combin. Theory Ser. A 43 5869.CrossRefGoogle Scholar
[4]Erdős, P. L., Füredi, Z. and Katona, G. O. H. (2005) Two-part and k-Sperner families: New proofs using permutations. SIAM J. Discrete Math. 19 489500.CrossRefGoogle Scholar
[5]Füredi, Z., Griggs, J. R., Odlyzko, A. M. and Shearer, J. M. (1987) Ramsey–Sperner theory. Discrete Math. 63 143152.CrossRefGoogle Scholar
[6]Katona, G. O. H. (1966) On a conjecture of Erdős and a stronger form of Sperner's theorem. Studia Sci. Math. Hungar. 1 5963.Google Scholar
[7]Katona, G. O. H. (2000) The cycle method and its limits. In Numbers, Information and Complexity (Althöfer, et al. , eds), Kluwer, pp. 129141.CrossRefGoogle Scholar
[8]Kleitman, D. J. (1965) On a lemma of Littlewood and Offord on the distribution of certain sums. Math. Z. 90 251259.CrossRefGoogle Scholar
[9]Shahriari, S. (1996) On the structure of maximum 2-part Sperner families. Discrete Math. 162 229238.CrossRefGoogle Scholar