Results 11 to 20 of about 473,238 (316)
Intersections and distinct intersections in cross-intersecting families
European Journal of Combinatorics, 2023 Let $\mathcal{F},\mathcal{G}$ be two cross-intersecting families of $k$-subsets of $\{1,2,\ldots,n\}$. Let $\mathcal{F}\wedge \mathcal{G}$, $\mathcal{I}(\mathcal{F},\mathcal{G})$ denote the families of all intersections $F\cap G$ with $F\in \mathcal{F},G\in \mathcal{G}$, and all distinct intersections $F\cap G$ with $F\neq G, F\in \mathcal{F},G\in ...
Peter Frankl, Jian Wang 0092
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The Intersection Spectrum of 3-Chromatic Intersecting Hypergraphs [PDF]
Proceedings of the London Mathematical Society, 2021 For a hypergraph $H$, define its intersection spectrum $I(H)$ as the set of all intersection sizes $|E\cap F|$ of distinct edges $E,F\in E(H)$. In their seminal paper from 1973 which introduced the local lemma, Erdős and Lovász asked: how large must the intersection spectrum of a $k$-uniform $3$-chromatic intersecting hypergraph be?
Bucić, Matija +2 more
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INTERACTING INTERSECTIONS [PDF]
International Journal of Modern Physics A, 1998 Intersecting p-branes can be viewed as higher-dimensional interpretations of multicharge extremal p-branes, where some of the individual p-branes undergo diagonal dimensional oxidation, while the others oxidize vertically. Although the naive vertical oxidation of a single p-brane gives a continuum of p-branes, a more natural description arises if one ...
Lü, H., Pope, C. N.
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Intersection Theorems with a Continuum of Intersection Points [PDF]
Journal of Optimization Theory and Applications, 1998 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Herings, P.J.J., Talman, A.J.J.
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Intersecting Braids and Intersecting Knot Theory [PDF]
Journal of Knot Theory and Its Ramifications, 1995 An extension of the Artin Braid Group is considered, with the introduction of new operatores that generate double and triple intersections. The extended Alexander theorem, relating intersecting closed braids and intersecting knots is proved for double and triple intersections, and a counter example is given for the case of quadruple intersections ...
Armand-Ugon, Daniel +2 more
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Counting Intersecting and Pairs of Cross-Intersecting Families [PDF]
Combinatorics, Probability and Computing, 2017 A family of subsets of {1,. . .,n} is calledintersectingif any two of its sets intersect. A classical result in extremal combinatorics due to Erdős, Ko and Rado determines the maximum size of an intersecting family ofk-subsets of {1,. . .,n}. In this paper we study the following problem: How many intersecting families ofk-subsets of {1,. .
Frankl, Péter, Kupavskii, Andrey
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The Intersection Structure of $t$-Intersecting Families [PDF]
The Electronic Journal of Combinatorics, 2005 A family of sets is $t$-intersecting if any two sets from the family contain at least $t$ common elements. Given a $t$-intersecting family of $r$-sets from an $n$-set, how many distinct sets of size $k$ can occur as pairwise intersections of its members? We prove an asymptotic upper bound on this number that can always be achieved.
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CoRR, 2023 Consider two regions in the plane, bounded by an $n$-gon and an $m$-gon, respectively. At most how many connected components can there be in their intersection? This question was asked by Croft. We answer this asymptotically, proving the bounds $$\left\lfloor \frac{m}{2}\right\rfloor \cdot \left\lfloor \frac{n}{2}\right\rfloor\le f(n,m)\le \left\lfloor
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Journal of Graph Theory, 2011 Summary: Let \(G\) and \(H\) be two graphs of order \(n\). If we place copies of \(G\) and \(H\) on a common vertex set, how much or little can they be made to overlap? The aim of this article is to provide some answers to this question, and to pose a number of related problems. Along the way, we solve a conjecture of \textit{P. Erdős} et al. [ibid. 12,
Bollobas, B, Scott, A
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Intersections of transformation [PDF]
Interactions, 2020 This forum is dedicated to exploring the notion of meaningfulness in design processes, taking the perspectives of community groups, nongovernmental organizations, and those who are marginalized in society as starting points. Authors will reflect conceptually and methodologically on practical engagements. --- Rosanna Bellini
Rosanna Bellini, Angelika Strohmayer
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