共查询到20条相似文献,搜索用时 15 毫秒
1.
Andrea Blunck 《Journal of Geometry》1996,56(1-2):9-17
The affine chain geometry over a group with a partial fibration into subgroups and a certain involution is introduced. This concept generalizes the affine trace of the chain geometry over an associative algebra. We study the geometric properties of these geometries and give examples.Dedicated to Professor Helmut Mäurer on the occasion of his 60th birthday 相似文献
2.
Martin Aigner 《Aequationes Mathematicae》1977,16(1-2):37-50
In a geometric lattice every interval can be mapped isomorphically into an upper interval (containing 1) by a strong map. A natural question thus arises as to what extent certain assumptions on the upper interval structure determine the whole lattice. We consider conditions of the following sort: that above a certain levelm any two upper intervals of the same length be isomorphic. This property, called uniformity, is studied for binary geometries. The geometries satisfying the strongest uniformity condition (m = 1) are determined (except for one open case). As is to be expected the corresponding problem for lower intervals is easier and is solved completely. 相似文献
3.
In this paper we prove that there exists an elliptic semiplaneS(v, k, m) withk –m 2 if and only if there exists a group divisible design GDD
k
((k –m)(k – 1);k –m; 0, 1) withm pairwise orthogonal resolutions. As an example of this theorem, we construct an elliptic semiplaneW(45, 7, 3) and show thatW is isomorphic to the elliptic semiplaneS(45, 7, 3) given by R. D. Baker. 相似文献
4.
We use a simple example (the projective plane on seven points) to give an introductory survey on the problems and methods in finite geometries — an area of mathematics related to geometry, combinatorial theory, algebra, group theory and number theory as well as to applied mathematics (e.g., coding theory, information theory, statistical design of experiments, tomography, cryptography, etc.). As this list already indicates, finite geometries is — both from the point of view of pure mathematics and from that of applications related to computer science and communication engineering — one of the most interesting and active fields of mathematics. It is the aim of this paper to introduce the nonspecialist to some of these aspects.To Professor Günter Pickert on the occasion of his 65th birthday 相似文献
5.
6.
Stephen Dow 《Combinatorica》1986,6(4):321-325
A partial affine plane (PAP) of ordern is ann
2-setS of points together with a collection ofn-subsets ofS called lines such that any two lines meet in at most one point. We obtain conditions under which a PAP with nearlyn
2+n lines can be completed to an affine plane by adding lines. In particular, we make use of Bruck’s completion condition for
nets to show that certain PAP’s with at leastn
2+n−√n can be completed and that forn≠3 any PAP withn
2+n−2 lines can be completed. 相似文献
7.
J. G. Oxley 《Periodica Mathematica Hungarica》1982,13(2):137-139
8.
Xiande Zhang 《Discrete Mathematics》2007,307(22):2786-2807
Partitionable skew Room frames of type hn have played an important role in the constructions of 4-frames, (K4-e)-frames and super-simple (4,2)-frames. In this paper, we investigate the existence of partitionable skew Room frames of type hn. The necessary conditions for the existence of such a design are that and h?5. It is proved that these necessary conditions are also sufficient with a few possible exceptions. As a byproduct, the known results on the existence of skew Room frames and uniform 4-frames are both improved. 相似文献
9.
Barbara Opozda 《Monatshefte für Mathematik》1996,121(1-2):113-124
A class of non-metrizable connections is studied. It contains the only non-flat locally symmetric connections existing on affine hypersurfaces of type number 1.The research was supported by the Alexander von Humboldt Stiftung and by the KBN grant no 2 P301 03004. 相似文献
10.
Within the concept of projective lattice geometry we are considering the class of stable geometries which have also been introduced in [14]. The investigation of their basic properties will result in fundamental structure theorems which especially give a lattice-geometric characterization of free left modules of rank 6 over proper right Bezout rings of stable rank 2. This yields a proper generalization of previous results of ours. 相似文献
11.
Aspread inPG(n, q) is a set of lines which partitions the point set. A packing inPG(n, q) (n odd) is a partition of the lines into spreads. Two packings ofPG(n, q) are calledorthogonal if and only if any two spreads, one from each packing, have at most one line in common. Recently, R. D. Baker has shown the existence of a pair of orthogonal packings inPG(5, 2). In this paper we enumerate all packings inPG(5, 2) having both an automorphism of order 31 and the Frobenius automorphism. We find all pairs of orthogonal packings of the above type and display a set of six mutually orthogonal packings. Previously the largest set of orthogonal packings known inPG(5, 2) was two. 相似文献
12.
13.
We partition the affine plane of order 7 into a set of M?bius-Kantor configurations 83 plus a set consisting only of one point. 相似文献
14.
Yoshihiro Mizuta 《Potential Analysis》2006,25(1):29-36
Our aim in this paper is to prove the existence of tangential limits for Poisson integrals of the fractional order of functions in the L p Hölder space on half spaces. 相似文献
15.
16.
In this paper we outline a construction method which has been used for minimal blocking sets in PG(2, q) and maximal partial line spreads in PG(n, q) and which must have a lot of more applications. We also give a survey on what is known about the spectrum of sizes of maximal
partial line spreads in PG(n, q). At the end we list some more elaborate random techniques used in finite geometry.
相似文献
17.
Thomas Binder 《Journal of Geometry》2004,79(1-2):31-45
We study non-degenerate affine surfaces in A3 with a projectively
flat induced connection. The curvature of the affine metric
, the affine
mean curvature H, and the Pick invariant
J are related by
.
Depending on the rank of the span of the gradients of these functions,
a local classification of three groups is given.
The main result is the characterization of the projectively flat but
not locally symmetric surfaces as a solution of a system of ODEs.
In the final part, we classify projectively flat and
locally symmetric affine translation surfaces. 相似文献
18.
Š. Porubský 《Periodica Mathematica Hungarica》1982,13(1):9-14
A necessary and sufficient condition for the group of isomorphisms involved in a factorization of a complete graph into isomorphic factors is established. 相似文献
19.
Li Fenggao 《高校应用数学学报(英文版)》2003,18(2):223-229
Let AG(n, F
q) be the n-dimensional affine space over F
q, where F
q is a finite field with q elements. Denote by Γ
(m) the graph induced by m-flats of AG(n, F
q). For any two adjacent vertices E and F of
is studied. In particular, sizes of maximal cliques in Γ
(m) are determined and it is shown that Γ
(m) is not edge-regular when m<n−1.
Supported by the National Natural Science Foundation of China (19571024) and Hunan Provincial Department of Education (02C512). 相似文献
20.
Donald E Knuth 《Journal of Combinatorial Theory, Series A》1974,16(3):398-400
A simple proof is given that limn?t8(log2 log2gn)/n = 1, where gn denotes the number of distinct combinatorial geometries on n point 相似文献