共查询到20条相似文献,搜索用时 31 毫秒
1.
Dhruv Mubayi 《Advances in Mathematics》2007,215(2):601-615
Fix integers n,r?4 and let F denote a family of r-sets of an n-element set. Suppose that for every four distinct A,B,C,D∈F with |A∪B∪C∪D|?2r, we have A∩B∩C∩D≠∅. We prove that for n sufficiently large, , with equality only if ?F∈FF≠∅. This is closely related to a problem of Katona and a result of Frankl and Füredi [P. Frankl, Z. Füredi, A new generalization of the Erd?s-Ko-Rado theorem, Combinatorica 3 (3-4) (1983) 341-349], who proved a similar statement for three sets. It has been conjectured by the author [D. Mubayi, Erd?s-Ko-Rado for three sets, J. Combin. Theory Ser. A, 113 (3) (2006) 547-550] that the same result holds for d sets (instead of just four), where d?r, and for all n?dr/(d−1). This exact result is obtained by first proving a stability result, namely that if |F| is close to then F is close to satisfying ?F∈FF≠∅. The stability theorem is analogous to, and motivated by the fundamental result of Erd?s and Simonovits for graphs. 相似文献
2.
Norihide Tokushige 《Journal of Combinatorial Theory, Series A》2007,114(4):575-596
Let 1?t?7 be an integer and let F be a k-uniform hypergraph on n vertices. Suppose that |A∩B∩C∩D|?t holds for all A,B,C,D∈F. Then we have if holds for some ε>0 and all n>n0(ε). We apply this result to get EKR type inequalities for “intersecting and union families” and “intersecting Sperner families.” 相似文献
3.
N. Castro-González J.Y. Vélez-Cerrada 《Journal of Mathematical Analysis and Applications》2008,341(2):1213-1223
Given a bounded operator A on a Banach space X with Drazin inverse AD and index r, we study the class of group invertible bounded operators B such that I+AD(B−A) is invertible and R(B)∩N(Ar)={0}. We show that they can be written with respect to the decomposition X=R(Ar)⊕N(Ar) as a matrix operator, , where B1 and are invertible. Several characterizations of the perturbed operators are established, extending matrix results. We analyze the perturbation of the Drazin inverse and we provide explicit upper bounds of ‖B?−AD‖ and ‖BB?−ADA‖. We obtain a result on the continuity of the group inverse for operators on Banach spaces. 相似文献
4.
Dhruv Mubayi 《Journal of Combinatorial Theory, Series A》2006,113(3):547-550
Fix integers k?3 and n?3k/2. Let F be a family of k-sets of an n-element set so that whenever A,B,C∈F satisfy |A∪B∪C|?2k, we have A∩B∩C≠∅. We prove that with equality only when ?F∈FF≠∅. This settles a conjecture of Frankl and Füredi [2], who proved the result for n?k2+3k. 相似文献
5.
Vladimir Nikiforov 《Discrete Mathematics》2010,310(1):125-131
In this note we complete an investigation started by Erd?s in 1963 that aims to find the strongest possible conclusion from the hypothesis of Turán’s theorem in extremal graph theory.Let be the complete r-partite graph with parts of sizes s1≥2,s2,…,sr with an edge added to the first part. Letting tr(n) be the number of edges of the r-partite Turán graph of order n, we prove that:For all r≥2 and all sufficiently small c>0, every graph of sufficiently large order n with tr(n)+1 edges contains a .We also give a corresponding stability theorem and two supporting results of wider scope. 相似文献
6.
7.
We survey results concerning the maximum size of a family F of subsets of an n-element set such that a certain configuration is avoided. When F avoids a chain of size two, this is just Sperner's theorem. Here we give bounds on how large F can be such that no four distinct sets A,B,C,D∈F satisfy A⊂B, C⊂B, C⊂D. In this case, the maximum size satisfies , which is very similar to the best-known bounds for the more restrictive problem of F avoiding three sets B,C,D such that C⊂B, C⊂D. 相似文献
8.
Rosihan M. Ali V. Ravichandran 《Journal of Mathematical Analysis and Applications》2006,324(1):663-668
Let A,B,D,E∈[−1,1]. Conditions on A,B,D and E are determined so that
9.
We consider a new type of extremal hypergraph problem: given an r-graph and an integer k≥2 determine the maximum number of edges in an -free, k-colourable r-graph on n vertices.Our motivation for studying such problems is that it allows us to give a new upper bound for an old Turán problem. We show that a 3-graph in which any four points span at most two edges has density less than , improving previous bounds of due to de Caen [D. de Caen, Extension of a theorem of Moon and Moser on complete subgraphs, Ars Combin. 16 (1983) 5–10], and due to Mubayi [D. Mubayi, On hypergraphs with every four points spanning at most two triples, Electron. J. Combin. 10 (10) (2003)]. 相似文献
10.
Chen-Lian Chuang 《Linear algebra and its applications》2011,435(12):3206-3211
Let D be a division algebra finite-dimensional over its center C and let A=Mm(D), the m×m matrix ring over D. By the length of a linear generalized polynomial (GP) ?(X), we mean the least positive integer n such that ?(X) can be represented in the form for some . We denote by L(?)=n the length of ?. By a central linear GP for A we mean a nonzero linear GP with central values on A. In this paper we characterize all central linear GPs for A and determine the lengths of all central linear GPs for A. 相似文献
11.
When A∈B(H) and B∈B(K) are given, we denote by MC the operator acting on the infinite dimensional separable Hilbert space H⊕K of the form . In this paper, it is shown that a 2×2 operator matrix MC is upper semi-Fredholm and ind(MC)?0 for some C∈B(K,H) if and only if A is upper semi-Fredholm and
12.
For X a compact Abelian group and B an infinite subset of its dual , let CB be the set of all x∈X such that converges to 1. If F is a free filter on , let . The sets CB and DF are subgroups of X. CB always has Haar measure 0, while the measure of DF depends on F. We show that there is a filter F such that DF has measure 0 but is not contained in any CB. This generalizes previous results for the special case where X is the circle group. 相似文献
13.
Preservers of spectral radius, numerical radius, or spectral norm of the sum on nonnegative matrices
Chi-Kwong Li 《Linear algebra and its applications》2009,430(7):1739-1398
Let be the set of entrywise nonnegative n×n matrices. Denote by r(A) the spectral radius (Perron root) of . Characterization is obtained for maps such that r(f(A)+f(B))=r(A+B) for all . In particular, it is shown that such a map has the form
14.
Lars Kadison 《Journal of Pure and Applied Algebra》2008,212(7):1822-1839
We introduce a notion of depth three tower C⊆B⊆A with depth two ring extension A|B being the case B=C. If and B|C is a Frobenius extension with A|B|C depth three, then A|C is depth two. If A, B and C correspond to a tower G>H>K via group algebras over a base ring F, the depth three condition is the condition that K has normal closure KG contained in H. For a depth three tower of rings, a pre-Galois theory for the ring and coring (A⊗BA)C involving Morita context bimodules and left coideal subrings is applied to specialize a Jacobson-Bourbaki correspondence theorem for augmented rings to depth two extensions with depth three intermediate division rings. 相似文献
15.
In [H. Krause, O. Solberg, Applications of cotorsion pairs, J. London Math. Soc. 68 (2003) 631-650], the Telescope Conjecture was formulated for the module category of an artin algebra R as follows: “If C=(A,B) is a complete hereditary cotorsion pair in with A and B closed under direct limits, then ”. We extend this conjecture to arbitrary rings R, and show that it holds true if and only if the cotorsion pair C is of finite type. Then we prove the conjecture in the case when R is right noetherian and B has bounded injective dimension (thus, in particular, when C is any cotilting cotorsion pair). We also focus on the assumptions that A and B are closed under direct limits and on related closure properties, and detect several asymmetries in the properties of A and B. 相似文献
16.
Janusz J. Charatonik Patricia Pellicer-Covarrubias 《Topology and its Applications》2007,154(2):333-338
Given a metric continuum X, let X2 denote the hyperspace of all nonempty closed subsets of X. For each positive integer k let Ck(X) stand for the hyperspace of members of X2 having at most k components. Consider mappings (where B∈Cm(X)) and both defined by A?A∪B. We give necessary and sufficient conditions under which these mappings are deformation retractions (under a special convention for φB). The conditions are related to the contractibility of the corresponding hyperspaces. 相似文献
17.
Z. Dong 《Journal of Mathematical Analysis and Applications》2011,377(2):631-644
We define the Haagerup property for C?-algebras A and extend this to a notion of relative Haagerup property for the inclusion B⊆A, where B is a C?-subalgebra of A. Let Γ be a discrete group and Λ a normal subgroup of Γ, we show that the inclusion A?α,rΛ⊆A?α,rΓ has the relative Haagerup property if and only if the quotient group Γ/Λ has the Haagerup property. In particular, the inclusion has the relative Haagerup property if and only if Γ/Λ has the Haagerup property; has the Haagerup property if and only if Γ has the Haagerup property. We also characterize the Haagerup property for Γ in terms of its Fourier algebra A(Γ). 相似文献
18.
Representation of the Drazin inverse for special block matrix 总被引:1,自引:0,他引:1
19.
Irène Charon 《Discrete Applied Mathematics》2006,154(8):1246-1253
Consider an oriented graph G=(V,A), a subset of vertices C⊆V, and an integer r?1; for any vertex v∈V, let denote the set of all vertices x such that there exists a path from x to v with at most r arcs. If for all vertices v∈V, the sets are all nonempty and different, then we call C an r-identifying code. We describe a linear algorithm which gives a minimum 1-identifying code in any oriented tree. 相似文献
20.
In this paper, we present a complement of a generalized Ando-Hiai inequality due to Fujii and Kamei [M. Fujii, E. Kamei, Ando-Hiai inequality and Furuta inequality, Linear Algebra Appl. 416 (2006) 541-545]. Let A and B be positive operators on a Hilbert space H such that 0<m1?A?M1 and 0<m2?B?M2 for some scalars mi?Mi (i=1,2), and let α∈[0,1]. Put for i=1,2. Then for each 0<r?1 and s?1