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1.
It has been close to ten years since the publication of Green's influential survey Finite field models in additive combinatorics [28], in which the author championed the use of high-dimensional vector spaces over finite fields as a toy model for tackling additive problems concerning the integers. The path laid out by Green has proven to be a very successful one to follow. In the present article we survey the highlights of the past decade and outline the challenges for the years to come. 相似文献
2.
Hugh Thomas 《Order》2006,23(2-3):249-269
In this paper, we study lattices that posess both the properties of being extremal (in the sense of Markowsky) and of being left modular (in the sense of Blass and Sagan). We call such lattices trim and show that they posess some additional appealing properties, analogous to those of a distributive lattice. For example, trimness is preserved under taking intervals and suitable sublattices. Trim lattices satisfy a weakened form of modularity. The order complex of a trim lattice is contractible or homotopic to a sphere; the latter holds exactly if the maximum element of the lattice is a join of atoms. Any distributive lattice is trim, but trim lattices need not be graded. The main example of ungraded trim lattices are the Tamari lattices and generalizations of them. We show that the Cambrian lattices in types A and B defined by Reading are trim; we conjecture that all Cambrian lattices are trim. 相似文献
3.
In this paper we introduce a generalization of stable sets: stable multi-sets. A stable multi-set is an assignment of integers
to the vertices of a graph, such that specified bounds on vertices and edges are not exceeded. In case all vertex and edge
bounds equal one, stable multi-sets are equivalent to stable sets.
For the stable multi-set problem, we derive reduction rules and study the associated polytope. We state necessary and sufficient
conditions for the extreme points of the linear relaxation to be integer. These conditions generalize the conditions for the
stable set polytope. Moreover, the classes of odd cycle and clique inequalities for stable sets are generalized to stable
multi-sets and conditions for them to be facet defining are determined.
The study of stable multi-sets is initiated by optimization problems in the field of telecommunication networks. Stable multi-sets
emerge as an important substructure in the design of optical networks.
Received: February 14, 2001/Revised version: September 7, 2001 相似文献
4.
Let {Xk}k?1 be a strictly stationary time series. For a strictly increasing sampling function g:?→? define Yk=Xg(k) as the deterministic sub‐sampled time series. In this paper, the extreme value theory of {Yk} is studied when Xk has representation as a moving average driven by heavy‐tailed innovations. Under mild conditions, convergence results for a sequence of point processes based on {Yk} are proved and extremal properties of the deterministic sub‐sampled time series are derived. In particular, we obtain the limiting distribution of the maximum and the corresponding extremal index. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
5.
Let G=(V,E) be a undirected k-edge connected graph with weights ce on edges and wv on nodes. The minimum 2-edge connected subgraph problem, 2ECSP for short, is to find a 2-edge connected subgraph of G, of minimum total weight. The 2ECSP generalizes the well-known Steiner 2-edge connected subgraph problem. In this paper we study the convex hull of the incidence vectors corresponding to feasible solutions of 2ECSP. First, a natural integer programming formulation is given and it is shown that its linear relaxation is not sufficient to describe the polytope associated with 2ECSP even when G is series-parallel. Then, we introduce two families of new valid inequalities and we give sufficient conditions for them to be facet-defining. Later, we concentrate on the separation problem. We find polynomial time algorithms to solve the separation of important subclasses of the introduced inequalities, concluding that the separation of the new inequalities, when G is series-parallel, is polynomially solvable. 相似文献
6.
V. S. Klimov 《Mathematical Notes》2007,81(1-2):61-71
We study homology characteristics of critical values and extremals of Lipschitz functionals defined on bounded closed convex subsets of a reflexive space that are invariant under deformations. Sufficient conditions for the existence of a bifurcation point of a multivalued potential operator (the switch principle for the typical number of an extremal) are established. 相似文献
7.
Masaaki Harada 《Designs, Codes and Cryptography》2006,38(1):5-16
In this paper, we show that the code generated by the rows of a block-point incidence matrix of a self-orthogonal 3-(56,12,65)
design is a doubly-even self-dual code of length 56. As a consequence, it is shown that an extremal doubly-even self-dual
code of length 56 is generated by the codewords of minimum weight. We also demonstrate that there are more than one thousand
inequivalent extremal doubly-even self-dual [56,28,12] codes. This result shows that there are more than one thousand non-isomorphic
self-orthogonal 3-(56,12,65) designs.
AMS Classification: 94B05, 05B05 相似文献
8.
Vasiliy A. Ustimenko 《Acta Appl Math》2002,74(2):117-153
A combinatorial method of encryption with a similarity to the classical scheme of linear coding has been suggested by the author. The general idea is to treat vertices of a graph as messages and arcs of a certain length as encryption tools. We will study the quality of such an encryption in the case of graphs of high girth by comparing the probability to guess the message, (vertex) at random with the probability of breaking the key, i.e. guessing the encoding arc. In fact, the quality is good for graphs which are close to the Erdös bound, defined by the Even Cycle Theorem.In the case of parallelotopic graphs, there is a uniform way to match arcs with strings in a certain alphabet. Among parallelotopic graphs we distinguish linguistic graphs of affine type whose vertices (messages) and arcs (encoding tools) both could be naturally identified with vectors over the GF(q), and neighbors of the vertex defined by a system of linear equations. We will discuss families of linguistic and parallelotopic graphs of increasing girth as the source for assymmetric cryptographic functions and related open key algorithms.Several constructions of families of linguistic graphs of high girth with good quality, complexity and expansion coefficients will be considered. Some of those constructions have been obtained via group-theoretical and geometrical techniques. 相似文献
9.
10.
A problem in extremal quasiconformal extensions 总被引:2,自引:0,他引:2
Yi Qi 《中国科学A辑(英文版)》1998,41(11):1135-1141
A constantK
0
(m)
(h) is introduced for every quasisymmetric mappingh of the unit circle and every integerm≥4 which contains the constantK
0(h) (indicated by the change in module of the quadrilaterals with vertices on the circle) as a special case. A necessary and
sufficient condition is established forK
0
(m)
(h) =K
1(h). It is shown that there are infinitely many quasisymmetric mappings of the unit circle having the property thatK
0
(m)
(h)<K
1(h), wherek
1(h) is the maximal dilatation ofh. 相似文献