Abstract
HAJNAL proved this statement in the case of l = 3 (unpublished). In this paper I prove for all cases that this is, indeed, the minimum, and find the (more complicated) minimum also for arbitrary n. The theorem is probably useful in proofs by induction over the maximal number of elements of the subsets in a system, as was SPERNER’S, lemma in his paper [1].
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Sperner, E.: Ein Satz über Untermengen einer endlichen Menge, Math. Z. 27 (1928) 544—548.
Ore, O.: Graphs and matching theorems, Duke Math. J. 22 (1955) 625—639.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Birkhäuser Boston, a part of Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Katona, G. (2009). A Theorem of Finite Sets. In: Gessel, I., Rota, GC. (eds) Classic Papers in Combinatorics. Modern Birkhäuser Classics. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4842-8_27
Download citation
DOI: https://doi.org/10.1007/978-0-8176-4842-8_27
Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-4841-1
Online ISBN: 978-0-8176-4842-8
eBook Packages: Springer Book Archive