منابع مشابه
Arcs on Spheres Intersecting at Most Twice
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).
متن کاملArcs 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...
متن کاملMost Probably Intersecting Hypergraphs
The celebrated Erdős-Ko-Rado theorem shows that for n > 2k the largest intersecting k-uniform set family on [n] has size ( n−1 k−1 ) . It is natural to ask how far from intersecting larger set families must be. Katona, Katona and Katona introduced the notion of most probably intersecting families, which maximise the probability of random subfamilies being intersecting. We consider the most prob...
متن کاملThe instability of intersecting fuzzy spheres
We discuss the stability of general configurations representing many fuzzy spheres in dimensionally reduced Yang-Mills-Chern-Simons models with and without supersymmetry. By performing one-loop perturbative calculations around such configurations, we find that intersecting fuzzy spheres are unstable in the class of models studied in this paper. We also obtain the large-N limit of the one-loop e...
متن کاملDisjoint Unit Spheres admit at Most Two Line Transversals
HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt età la diffusion de documents scientifiques de niveau r...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Indiana University Mathematics Journal
سال: 2019
ISSN: 0022-2518
DOI: 10.1512/iumj.2019.68.7565