A theorem of finite sets

By G. Katona. 2009

355 citations recorded by the source corpus.

Subfields: Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/27f7c840b56a76adad44d8e2342c02a91e3803c6

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Electrical and Electronic Engineering

Citations in the corpus

Upper tails via high moments and entropic stability (2019, result): “This is a weak version of a more precise result due to Erdős–Hanani [29] and also follows from the Kruskal–Katona theorem [44, 49].”
Stability versions of Erdős–Ko–Rado type theorems via isoperimetry (2016, methodology): “(This argument relies upon the full Kruskal-Katona theorem [41, 47], for which a t-umvirate is fortunately extremal.”
Socles of Buchsbaum modules, complexes and posets (2007, methodology): “One can then envoke the Kruskal-Katona theorem [14, 17] and the Clements-Lindsröm theorem [6], respectively, instead of Macaulay’s theorem, to replace the bound hj+1 ≤ (hj − ( d j ) βj−1) <j> with stronger bounds, namely, with hj+1 ≤ (hj − ( d j ) βj−1)) (j) in the balanced case, and with hj+1 ≤ (hj”
Shadows and intersections: Stability and new proofs (2008, neutral): “The Kruskal–Katona theorem [ 19 ,22] is a classical result in Extremal Combinatorics that gives a tight lower bound on the size of the shadow of a k-graph.1 It states that |∂G| |∂G0|, where G0 is the initial segment of length |G| in the colexicographic order2 on k-tuples of some ordered set.”
Extremal t‐intersecting sub‐families of hereditary families (2009, methodology): “There are various proofs of this theorem, two of which are particularly short and beautiful: Katona’s [31] using the cycle method and Daykin’s [12] using a fundamental result known as the Kruskal– Katona theorem [30, 33].”
Surveys in Combinatorics 2011: Hypergraph Turán problems (2011, methodology): “In general the extremal example is determined by the Kruskal-Katona theorem [118, 100].”
Experiment selection for causal discovery (2013, background): “The question then becomes, how can we choose as many sets as possible of size l − 1, thus minimizing the number of sets needed of size l, nevertheless obtaining a valid antichain? From the Kruskal-Katona Theorem (Kruskal, 1963; Katona, 1968) it follows that an optimal solution can be obtained by cho”