๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Yet another generalization of the Kruskal-Katona theorem

โœ Scribed by G.F. Clements


Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
479 KB
Volume
184
Category
Article
ISSN
0012-365X

No coin nor oath required. For personal study only.

โœฆ Synopsis


The rank r(a) of a is b{ila/= tn}l. For 0 ~<l~<n, the set consisting of all elements of rank l is called the lth rank and is denoted /}. Let b, l and m denote positive integers satisfying b ~ l ~<n and m ~<ITII. For a subset .~ยข of Tt, Ab.~ denotes the elements of Tt-b which precede at least one element of s~ยข. An algorithm is given for calculating min labial, where the minimum is taken over all m-element subsets .~ of ~. If tl = t2 .....


๐Ÿ“œ SIMILAR VOLUMES


A new proof of the colored Kruskalโ€”Katon
โœ Eran London ๐Ÿ“‚ Article ๐Ÿ“… 1994 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 386 KB

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.

A Kruskalโ€“Katona Type Theorem for the Li
โœ S Bezrukov; A Blokhuis ๐Ÿ“‚ Article ๐Ÿ“… 1999 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 154 KB

We present an analog of the well-known Kruskal-Katona theorem for the poset of subspaces of PG(n, 2) ordered by inclusion. For given k, (k < ) and m the problem is to find a family of size m in the set of -subspaces of PG(n, 2), containing the minimal number of k-subspaces. We introduce two lexicogr

A new short proof for the Kruskal-Katona
โœ P Frankl ๐Ÿ“‚ Article ๐Ÿ“… 1984 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 96 KB

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.