共查询到20条相似文献,搜索用时 15 毫秒
1.
Eva Ferrara Dentice 《Journal of Geometry》1996,55(1-2):73-85
In this paper a complete classification of finite matroids with one more hyperplane than points is obtained.Dedicated to Professor Maria Scafati Tallini on the occasion of her 65th birthday 相似文献
2.
A famous result of de Bruijn and Erdős (Indag. Math. 10 (1948) 421–423) states that a finite linear space has at least as many lines as points, with equality only if it is a projective plane or a near-pencil. This result led to the problem of characterizing finite linear spaces for which the difference between the number b of lines and the number v of points is assigned.
In this paper finite linear spaces with b−vm, m being the minimum number of lines on a point, are characterized. 相似文献
3.
Michel Lavrauw Leo Storme Geertrui Van de Voorde 《Designs, Codes and Cryptography》2008,48(3):231-245
In this paper, we study the p-ary linear code C(PG(n,q)), q = p
h
, p prime, h ≥ 1, generated by the incidence matrix of points and hyperplanes of a Desarguesian projective space PG(n,q), and its dual code. We link the codewords of small weight of this code to blocking sets with respect to lines in PG(n,q) and we exclude all possible codewords arising from small linear blocking sets. We also look at the dual code of C(PG(n,q)) and we prove that finding the minimum weight of the dual code can be reduced to finding the minimum weight of the dual
code of points and lines in PG(2,q). We present an improved upper bound on this minimum weight and we show that we can drop the divisibility condition on the
weight of the codewords in Sachar’s lower bound (Geom Dedicata 8:407–415, 1979).
G. Van de Voorde’s research was supported by the Institute for the Promotion of Innovation through Science and Technology
in Flanders (IWT-Vlaanderen). 相似文献
4.
5.
K. S. Kobylkin 《Proceedings of the Steklov Institute of Mathematics》2015,289(1):126-138
We consider the NP-hard problem of polyhedral separability of two finite sets A and B of points in general position in ? d by the minimum number of hyperplanes in the sense of a boolean function from a given class Σ. Both deterministic and probabilistic lower bounds are obtained for this number for two different classes of functions Σ. 相似文献
6.
Nicola Durante 《Journal of Geometry》2001,70(1-2):44-58
In this paper finite {s-2, s}-semiaffine linear spaces of order n are studied. It is proved that if s= 6 or then there is only a finite number of such linear spaces. Received 28 May 1999; revised 28 December 1999. 相似文献
7.
In this paper, we study the p-ary linear code Ck(n,q), q=ph, p prime, h1, generated by the incidence matrix of points and k-dimensional spaces in PG(n,q). For kn/2, we link codewords of Ck(n,q)Ck(n,q) of weight smaller than 2qk to k-blocking sets. We first prove that such a k-blocking set is uniquely reducible to a minimal k-blocking set, and exclude all codewords arising from small linear k-blocking sets. For k<n/2, we present counterexamples to lemmas valid for kn/2. Next, we study the dual code of Ck(n,q) and present a lower bound on the weight of the codewords, hence extending the results of Sachar [H. Sachar, The Fp span of the incidence matrix of a finite projective plane, Geom. Dedicata 8 (1979) 407–415] to general dimension. 相似文献
8.
Hans-Joachim Pohl 《Journal of Geometry》1990,38(1-2):107-157
All flat projective planes whose collineation group contains a 2-dimensional subgroup fixing at least two lines and more than two points are classified. Furthermore, all isomorphism types of such planes are determined. This completes the classification of all flat projective planes admitting a 2-dimensional collineation group. 相似文献
9.
Possession of a unique nonidentity commutator/associator is a property that dominates the theory of loops whose loop rings, while not associative, nevertheless satisfy an “interesting” identity. For instance, until now, all loops with loop rings satisfying the right Bol identity (such loops are called SRAR) have been known to have this property. In this paper, we present various constructions of other kinds of SRAR loops. 相似文献
10.
E. A. Sevost’yanov 《Ukrainian Mathematical Journal》2010,62(2):241-258
It is shown that if a point x
0 ∊ ℝ
n
, n ≥ 3, is an essential isolated singularity of an open discrete Q-mapping f : D →
[`(\mathbb Rn)] \overline {\mathbb {R}^n} , B
f
is the set of branch points of f in D; and a point z
0 ∊
[`(\mathbb Rn)] \overline {\mathbb {R}^n} is an asymptotic limit of f at the point x
0; then, for any neighborhood U containing the point x
0; the point z
0 ∊ [`(f( Bf ?U ))] \overline {f\left( {B_f \cap U} \right)} provided that the function Q has either a finite mean oscillation at the point x
0 or a logarithmic singularity whose order does not exceed n − 1: Moreover, for n ≥ 2; under the indicated conditions imposed on the function Q; every point of the set
[`(\mathbb Rn)] \overline {\mathbb {R}^n} \ f(D) is an asymptotic limit of f at the point x
0. For n ≥ 3, the following relation is true:
[`(\mathbbRn )] \f( D ) ì [`(f Bf )] \overline {\mathbb{R}^n } \backslash f\left( D \right) \subset \overline {f\,B_f } . In addition, if ¥ ? f( D ) \infty \notin f\left( D \right) , then the set f
B
f
is infinite and x0 ? [`(Bf )] x_0 \in \overline {B_f } . 相似文献
11.
Pietro Belotti Julio C. Góez Imre Pólik Ted K. Ralphs Tamás Terlaky 《Discrete Applied Mathematics》2013,161(16-17):2778-2793
We investigate families of quadrics all of which have the same intersection with two given hyperplanes. The cases when the two hyperplanes are parallel and when they are nonparallel are discussed. We show that these families can be described with only one parameter and describe how the quadrics are transformed as the parameter changes. This research was motivated by an application in mixed integer conic optimization. In that application, we aimed to characterize the convex hull of the union of the intersections of an ellipsoid with two half-spaces arising from the imposition of a linear disjunction. 相似文献
12.
证明了对于q≥17,当4q~5-5q~4-2q+1≤d≤4q~5-5q~4-q时,不存在达到Griesmer界的[n,k,d]_q码.此结果推广了Cheon等人在2005年和2008年的非存在性定理. 相似文献
13.
Let M1 and M2 be two matroids on the same ground set S. We conjecture that if there do not exist disjoint subsets A1,A2,…,Ak+1 of S, such that ispM1(Ai)≠Ø, and similarly for M2, then S is partitioned into k sets, each independent in both M1 and M2. This is a possible generalization of König's edge-coloring theorem. We prove the conjecture for the case k=2 and for a regular case, in which both matroids have the same rank d, and S consists of k·d elements. Finally, we prove another special case related to a conjecture of Rota. 相似文献
14.
《Operations Research Letters》2019,47(5):363-365
Kalai and Kalai (2013) presented five axioms for solutions of 2-person semi-cooperative games: games in which the basic data specifies individual strategies and payoffs, but in which the players can sign binding contracts and make utility transfers. The axioms pin down a unique solution, the coco value. I show that if one adds a mild dummy player axiom to the list, then the axioms become inconsistent when there are more than two players. 相似文献
15.
16.
E. Capelas de Oliveira Ary O. Chiacchio 《International Journal of Mathematical Education in Science & Technology》2013,44(4):491-497
The paper considers a class of real integrals performed by using a convenient integral in the complex plane. A complex integral containing a multi-valued function with two branch points is transformed into another integral containing a pole and a unique branch point. As a by-product we obtain a new class of integrals which can be calculated in a very simple way. 相似文献
17.
Vania Mascioni 《Discrete Mathematics》2005,300(1-3):129-138
For a set of 3 or 4 points we compute the exact probability that, after assigning the distances between these points uniformly at random from the set 1,…,n , the space obtained is metric. The corresponding results for random real distances follow easily. We also prove estimates for the general case of a finite set of points with uniformly random real distances. 相似文献
18.
Let ? be a primitive substitution on a two-letter alphabet {a,b} having two fixed points ξa and ξb. We show that the substitution ? is invertible if and only if one has ξa=abξ and ξb=baξ. To cite this article: Z.-X. Wen et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 727–731. 相似文献
19.
In this paper we prove that a set of points (in a projective space over a finite field of q elements), which is incident with 0 mod r points of every hyperplane, has at least (r−1)q+(p−1)r points, where 1<r<q=ph, p prime. An immediate corollary of this theorem is that a linear code whose weights and length have a common divisor r<q and whose dual minimum distance is at least 3, has length at least (r−1)q+(p−1)r. The theorem, which is sharp in some cases, is a strong generalisation of an earlier result on the non-existence of maximal arcs in projective planes; the proof involves polynomials over finite fields, and is a streamlined and more transparent version of the earlier one. 相似文献
20.
Let a set of points in the Euclidean plane be given. We are going to investigate the levels of the function measuring the sum of distances from the elements of the pointset which are called foci. Levels with only one focus are circles. In case of two different points as foci they are ellipses in the usual sense. If the set of the foci consists of more than two points then we have the so-called polyellipses. In this paper we investigate them from the viewpoint of differential geometry. We give a lower and upper bound for the curvature involving explicit constants. They depend on the number of the foci, the rate of the level and the global minimum of the function measuring the sum of the distances. The minimizer will be characterized by a theorem due to E. Weiszfeld together with a new proof. Explicit examples will also be given. As an application we present a new proof for a theorem due to P. Erd?s and I. Vincze. The result states that the approximation of a regular triangle by circumscribed polyellipses has an absolute error in the sense that there is no way to exceed it even if the number of the foci are arbitrary large. 相似文献