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Moments of Gaps Between k-Free Numbers

✍ Scribed by S.W. Graham

Publisher
Elsevier Science
Year
1993
Tongue
English
Weight
296 KB
Volume
44
Category
Article
ISSN
0022-314X

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πŸ“œ SIMILAR VOLUMES

On Gaps Between k-Free Numbers
On Gaps Between k-Free Numbers
✍ O. Trifonov πŸ“‚ Article πŸ“… 1995 πŸ› Elsevier Science 🌐 English βš– 337 KB

An elementary proof is given that for \(k \geqslant 3\) there exists a constant \(c=c(k)\) such that for \(x\) sufficiently large (depending on \(k\) ), the interval \(\left(x, x+c x^{1,12 k+1} \log x\right.\) ] contains a \(k\)-free number. This result improves on a previous result of M. Filaseta (

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✍ JΓΌrgen Eckhoff πŸ“‚ Article πŸ“… 1999 πŸ› Elsevier Science 🌐 English βš– 448 KB

Let v, e and t denote the number of vertices, edges and triangles, respectively, of a K4-free graph. Fisher (1988) proved that t<,(e/3) 3/2, independently of v. His bound is attained when e = 3k 2 for some integer k, but not in general. We find here, for any given value of e, the maximum possible va

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A gap between the appearances of a k-core and a (k + 1)-chromatic graph
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We observe that the values of p for which with high probability Gm,p is k-colorable and for which with high probability G,,p has no k-core are not equal for k 2 4.