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...

In this paper, we prove strong approximations for the (MAPt/PHt/∞) queueing network. These strong approximations allow us to derive fluid and diffusion limits for the queue length processes of the network. This extends recent work by Ko and Pender [9], which provides fluid and diffusion limits in the single station setting.

We survey conjectured and proven Ahlswede-type higher-order generalizations of the Erdős-Ko-Rado theorem.

Zeng-Hua Li, Lie-Wen Chen, 2 Che Ming Ko, Bao-An Li, and Hong-Ru Ma Institute of Theoretical Physics, Shanghai Jiao Tong University, Shanghai 200240, China Center of Theoretical Nuclear Physics, National Laboratory of Heavy Ion Accelerator, Lanzhou 730000, China Cyclotron Institute and Physics Department, Texas A&M University, College Station, Texas 77843-3366, USA Department of Physics, Texas ...

LetX be a proper variety defined over a fieldK. Following [Manin72], two points x, x ∈ X(K) are called R-equivalent if they can be connected by a chain of rational curves defined over K, cf. (4.1). In essence, two points are R-equivalent if they are “obviously” rationally equivalent. Several authors have proved finiteness results over local and global fields (cubic hypersurfaces [Manin72, Swinn...

A family A of sets is said to be intersecting if A ∩ B = ∅ for every A,B ∈ A. For a family F of sets, let ex(F) := {A ⊆ F : A is a largest intersecting subfamily of F}. For n ≥ 0 and r ≥ 0, let [n] := {i ∈ N : i ≤ n} and ([n] r ) := {A ⊆ [n] : |A| = r}. For a sequence {di}i∈N of non-negative integers that is monotonically non-decreasing (i.e. di ≤ di+1 for all i ∈ N), let P({di}i∈N) := {{a1, . ...

Exemple : 1 ère itération : travail administratif 2 ème itération : responsabilité de travail-administratif À chaque itération, les collocations binaires (et ternaires pour les collocations prépositionnelles) sont sélectionnées avec une mesure statistique et l'ajout de paramètres [Roche et al., 2004]. Corpus étudiés :-Corpus de Ressources Humaines (société PerformanSe) – 3784 Ko (en français)-C...

Intersection properties of sets have been widely investigated by many authors. One type of theorems proved for them has the following form [9]. Let S be an n-element set and AI. ... , AN £ S, 1 £ [1, n]. Assume that IAi I1Ajl E 1 for 1,,;;;; i <j ,,;;;;N. How large can N be under this condition, depending on n and I? Thus, e.g., the de Bruijn-Erdos theorem [1] asserts that if IAi I1Ajl = 1 for ...

A recent framework for generalizing the Erdős-KoRado Theorem, due to Holroyd, Spencer, and Talbot, defines the Erdős-Ko-Rado property for a graph in terms of the graph’s independent sets. Since the family of all independent sets of a graph forms a simplicial complex, it is natural to further generalize the Erdős-Ko-Rado property to an arbitrary simplicial complex. An advantage of working in sim...