We give a very short proof for the Kruskal-Katona theorem and Lovhsz's version of it: given (~) k-element sets there are at least (k~\_l) (k -1)-element sets which are contained in at least one of the k-sets.
A new proof of the colored Kruskal—Katona theorem
✍ Scribed by Eran London
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 386 KB
- Volume
- 126
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
✦ Synopsis
An extension of the Kruskal-Katona theorem to colored hypergraphs was given by Frankl, Fiiredi and Kalai in [Shadows of colored complexes, Mathematics Scandinavica]. Here we give a new simple proof.
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