Results 1  10
of
156
On crossintersecting families of independent sets in graphs
"... Let A1,...,Ak be a collection of families of subsets of an nelement set. We say that this collection is crossintersecting if for any i, j ∈ [k] with i = j, A ∈Ai and B ∈Aj implies A ∩ B = ∅. We consider a theorem of Hilton which gives a best possible upper bound on the sum of the cardinalities o ..."
Abstract
 Add to MetaCart
of uniform crossintersecting families. We formulate a graphtheoretic analogue of Hilton’s crossintersection theorem, similar to the one developed by Holroyd, Spencer and Talbot for the ErdősKoRado theorem. In particular we build on a result of Borg and Leader for signed sets and prove a theorem
On disjoint crossing families in geometric graphs, Electronic
"... A geometric graph is a graph drawn in the plane with vertices represented by points and edges as straightline segments. A geometric graph contains a (k, l)crossing family if there is a pair of edge subsets E1, E2 such that E1  = k and E2  = l, the edges in E1 are pairwise crossing, the edges ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
nvertex geometric graph with no (k, k)crossing family has at most ckn log n edges, where ck is a constant that depends only on k, by proving a more general result which relates extremal function of a geometric graph F with extremal function of two completely disjoint copies of F. We also settle
A special class of almost disjoint families
 J. Symb. Log
, 1995
"... Abstract. The collection of branches (maximal linearly ordered sets of nodes) of the tree <ω ω (ordered by inclusion) forms an almost disjoint family (of sets of nodes). This family is not maximal – for example, any level of the tree is almost disjoint from all of the branches. How many sets must ..."
Abstract

Cited by 9 (0 self)
 Add to MetaCart
must be added to the family of branches to make it maximal? This question leads to a series of definitions and results: a set of nodes is offbranch if it is almost disjoint from every branch in the tree; an offbranch family is an almost disjoint family of offbranch sets; o is the minimum cardinality
Disjoint common transversals and exchange structures
 J. London Math. Soc
, 1976
"... We state and prove a theorem (Theorem 1 below) which strengthens previously known results concerning disjoint common partial transversals of two families of sets. This theorem may be viewed as a result on transversal preindependence structures. We define a "disjointexchange structure & ..."
Abstract

Cited by 7 (0 self)
 Add to MetaCart
We state and prove a theorem (Theorem 1 below) which strengthens previously known results concerning disjoint common partial transversals of two families of sets. This theorem may be viewed as a result on transversal preindependence structures. We define a "disjointexchange structure
Materials for an exploratory theory of the network society.
 The British Journal of Sociology
, 2000
"... ABSTRACT This article aims at proposing some elements for a grounded theor y of the network society. The network society is the social structure characteristic of the Information Age, as tentatively identi ed by empirical, crosscultural investigation. It permeates most societies in the world, in v ..."
Abstract

Cited by 122 (0 self)
 Add to MetaCart
ABSTRACT This article aims at proposing some elements for a grounded theor y of the network society. The network society is the social structure characteristic of the Information Age, as tentatively identi ed by empirical, crosscultural investigation. It permeates most societies in the world
CROSS tINTERSECTING INTEGER SEQUENCES FROM WEIGHTED ERDŐS–KO–RADO
, 2013
"... Let m, n and t be positive integers. Consider [m] n as the set of sequences of length n on an mletter alphabet. We say that two subsets A ⊂ [m] n and B ⊂ [m] n cross tintersect if any two sequences a ∈ A and b ∈ B match in at least t positions. In this case it is shown that if m> (1 − 1 t √ 2)− ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
)−1 then AB  ≤ (m n−t) 2. We derive this result from a weighted version of the Erdős–Ko–Rado theorem concerning cross tintersecting families of subsets, and we also include the corresponding stability statement. One of our main tools is the eigenvalue method for intersection matrices due to Friedgut [10].
Intersecting families of permutations
 Journal of the American Mathematical Society
"... A set of permutations I ⊂ Sn is said to be kintersecting if any two permutations in I agree on at least k points. We show that for any k ∈ N, if n is sufficiently large depending on k, then the largest kintersecting subsets of Sn are cosets of stabilizers of k points, proving a conjecture of Deza ..."
Abstract

Cited by 27 (6 self)
 Add to MetaCart
and Frankl. We also prove a similar result concerning kcrossintersecting subsets. Our proofs are based on eigenvalue techniques and the representation theory of the symmetric group. 1
NORMAL FAMILIES OF MEROMORPHIC FUNCTIONS CONCERNING DIFFERENTIAL POLYNOMIALS
"... Abstract. Huang and Gu[10] proved that a family F of meromorphic functions in a domain D is normal, if, for two analytic functions a(z)(̸ ≡ 0), b(z) in D and all f ∈ F, (1) f(z) ̸ = ∞ when a(z) = 0;(2) f ′ (z) − a(z)f 2 (z) ̸ = b(z); (3) all poles of f(z) are of multiplicity at least 4. In this p ..."
Abstract
 Add to MetaCart
. In this paper, we first give an example to show that condition (3) is sharp, and prove that our counterexample is unique in some sense. Also, two normality criteria are given, which extend the result of Huang and Gu. 1.
SHARP BILINEAR ESTIMATES AND WELLPOSEDNESS FOR THE 1D SCHRÖDINGERDEBYE SYSTEM
, 2006
"... Abstract. We establish local and global wellposedness for the initial value problem associated to the (onedimensional) SchrödingerDebye (SD) system for data in the Sobolev spaces with low regularity. To obtain local results we prove two new sharp bilinear estimates for the coupling terms of this ..."
Abstract
 Add to MetaCart
of this system in the continuous and periodic cases. Concerning global results, the system is shown to be globally wellposed in H s × H s, −1/8 < s < 0. This is quite surprising in view of Bidegaray’s theorem: in H s × H s, s> 5/2, there are oneparameter families of solutions of the SD system
Mad families and their neighbors
, 2007
"... Abstract. We study several sorts of maximal almost disjoint families, both on a countable set and on uncountable, regular cardinals. We relate the associated cardinal invariants with bounding and dominating numbers and also with the uniformity of the meager ideal and some of its generalizations. 1. ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
of functions and of permutations. Although part of our work (Section 5) is concerned with mad families on the set ω of natural numbers, most of what we do is in the context of arbitrary regular cardinals. Indeed, some of our results extend to
Results 1  10
of
156