منابع مشابه
Arcs Intersecting at Most Once
We prove that on a punctured oriented surface with Euler characteristic χ < 0, the maximal cardinality of a set of essential simple arcs that are pairwise nonhomotopic and intersecting at most once is 2|χ|(|χ|+1). This gives a cubic estimate in |χ| for a set of curves pairwise intersecting at most once on a closed surface. We also give polynomial estimates in |χ| for sets of arcs and curves pai...
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Let p be a puncture of a punctured sphere, and let Q be the set of all other punctures. We prove that the maximal cardinality of a set A of arcs pairwise intersecting at most once, which start at p and end in Q, is |χ|(|χ| + 1). We deduce that the maximal cardinality of a set of arcs with arbitrary endpoints pairwise intersecting at most twice is |χ|(|χ|+ 1)(|χ|+ 2).
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Let F be a family of an n-element set. It is called intersecting if every pair of its members have a non-disjoint intersection. It is wellknown that an intersecting family satisfies the inequality |F| ≤ 2n−1. Suppose that |F| = 2n−1+i. Choose the members of F independently with probability p (delete them with probability 1−p). The new family is intersecting with a certain probability. We try to...
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ژورنال
عنوان ژورنال: Designs, Codes and Cryptography
سال: 2019
ISSN: 0925-1022,1573-7586
DOI: 10.1007/s10623-019-00699-6