1,070 research outputs found
On the number of maximal intersecting k-uniform families and further applications of Tuza's set pair method
We study the function which denotes the number of maximal
-uniform intersecting families . Improving a
bound of Balogh at al. on , we determine the order of magnitude of
by proving that for any fixed , holds. Our proof is based on Tuza's set pair
approach.
The main idea is to bound the size of the largest possible point set of a
cross-intersecting system. We also introduce and investigate some related
functions and parameters.Comment: 11 page
Systoles and kissing numbers of finite area hyperbolic surfaces
We study the number and the length of systoles on complete finite area
orientable hyperbolic surfaces. In particular, we prove upper bounds on the
number of systoles that a surface can have (the so-called kissing number for
hyperbolic surfaces). Our main result is a bound which only depends on the
topology of the surface and which grows subquadratically in the genus.Comment: A minor mistake and a computation fixed, small changes in the
exposition. 23 pages, 13 figure
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