منابع مشابه
Forbidding Just One Intersection
Following a conjecture of P. Erdos, we show that if 9 is a family of k-subsets of an n-set no two of which intersect in exactly I elements then for k 2 21+ 2 and n sufficiently large IF:/ < (;:‘,I:) with equality holding if and only if 9 consists of all the k-sets containing a fixed (I+ I)-set. In general we show 19) <dknmax(‘.k-‘-l), where dk is a constant depending only on k. These results ar...
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A family A ⊂ P[n] is said to be an antichain if A 6⊂ B for all distinct A,B ∈ A. A classic result of Sperner shows that such families satisfy |A| ≤ ( n bn/2c ) , which is easily seen to be best possible. One can view the antichain condition as a restriction on the intersection sizes between sets in different layers of P[n]. More generally one can ask, given a collection of intersection restrict...
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The term brain activity refers to a wide range of mental faculties that can be assessed either on anatomical/functional micro-, mesoand macrospatiotemporal scales of observation, or on intertwined levels with mutual interactions. Here we show, based on novel topological findings, how every brain activity encompassed in a given anatomical or functional level necessarily displays a counterpart in...
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We consider an extremal problem motivated by a paper of Balogh [J. Balogh, A remark on the number of edge colorings of graphs, European Journal of Combinatorics 27, 2006, 565–573], who considered edge-colorings of graphs avoiding fixed subgraphs with a prescribed coloring. More precisely, given r ≥ t ≥ 2, we look for n-vertex graphs that admit the maximum number of r-edge-colorings such that at...
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The purpose of this contribution1 is to set up a language to evaluate the results of concerted action among interdependent agents against predetermined properties that we can recognise as desirable from a deontic point of view. Unlike the standard view of logics to reason about coalitionally rational action, the capacity of a set of agents to take a rational decision will be restricted to what ...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1985
ISSN: 0097-3165
DOI: 10.1016/0097-3165(85)90035-4