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A Splitting Inequality (1998)

McColm, Gregory L.

Springer

The Ramanujan journal 2 (1998), S. 511-519

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ISSN: 1572-9303

Keywords: Bollobás-Thomason theorem ; Kruskal-Katona theorem ; splitting arguments ; splitting inequalities ; threshold functions ; upward-closed properties

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract We prove that if A is a finite set, and if $$\mathcal{F}$$ is an downwards-closed family of subsets of A, and if fx is the proportion of x-element subsets of A in $$\mathcal{F}$$ , then fa · fb ≤ fa + b − r, if r 〈 $$ \frac{{ab}}{{\left| A \right|}} $$ . We connect this result with the Weak Threshold Theorem.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1023/A:1009737027936

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