共查询到20条相似文献,搜索用时 15 毫秒
1.
Albrecht Beutelspacher 《Journal of Geometry》1986,26(1):43-61
In this paper we shall classify all finite linear spaces with line degrees n and n-k having at most n2+n+1 lines. As a consequence of this classification it follows: If n is large compared with k, then any such linear space can be embedded in a projective plane of order n–1 or n. 相似文献
2.
3.
In this paper, a common characterization of the finite projective space of dimension four and order \(n\) and of a finite inversive plane of order \(n+1\) in terms of regular \((k,n)\) finite planar spaces is given.
相似文献4.
We discuss some recent results of us regarding a class of polar spaces which includes the nonembeddable polar spaces introduced by Tits [Tits, J., “Buildings of spherical type and finite BN-pairs,” Lecture Notes in Mathematics 386, Springer-Verlag, Berlin-New York, 1974]. These results include an elementary construction of the polar space, a construction of a polarized embedding of the corresponding dual polar space and the determination whether this projective embedding is universal and unique (as a polarized embedding). 相似文献
5.
Scott P. Randby 《Journal of Graph Theory》1997,25(2):153-163
We show that if G is a graph embedded on the projective plane in such a way that each noncontractible cycle intersects G at least n times and the embedding is minimal with respect to this property (i.e., the representativity of the embedding is n), then G can be reduced by a series of reduction operations to an n × n × n projective grid. The reduction operations consist of changing a triangle of G to a triad, changing a triad of G to a triangle, and several others. We also show that if every proper minor of the embedding has representativity < n (i.e., the embedding is minimal), then G can be obtained from an n × n × n projective grid by a series of the two reduction operations described above. Hence every minimal embedding has the same number of edges. © 1997 John Wiley & Sons, Inc. J Graph Theory 25: 153–163, 1997 相似文献
6.
Aart Blokhuis 《Journal of Combinatorial Theory, Series A》2011,118(4):1228-1238
We investigate finite 3-nets embedded in a projective plane over a (finite or infinite) field of any characteristic p. Such an embedding is regular when each of the three classes of the 3-net comprises concurrent lines, and irregular otherwise. It is completely irregular when no class of the 3-net consists of concurrent lines. We are interested in embeddings of 3-nets which are irregular but the lines of one class are concurrent. For an irregular embedding of a 3-net of order n?5 we prove that, if all lines from two classes are tangent to the same irreducible conic, then all lines from the third class are concurrent. We also prove the converse provided that the order n of the 3-net is smaller than p. In the complex plane, apart from a sporadic example of order n=5 due to Stipins [7], each known irregularly embedded 3-net has the property that all its lines are tangent to a plane cubic curve. Actually, the procedure of constructing irregular 3-nets with this property works over any field. In positive characteristic, we present some more examples for n?5 and give a complete classification for n=4. 相似文献
7.
Vito Napolitano 《Rendiconti del Circolo Matematico di Palermo》2001,50(3):443-454
A well known result on finite linear spaces due to de Bruijn and Erdös states that the numberb of lines is greater than or equal to the numberv of points, withb=v if and only if the linear space is either a near pencil, or a projective plane. The problem of characterizing finite linear spaces with small deficienciess=b?v has been investigated by several authors, especially by Bridges forb=v+1 and de Witte forb=v+2. In this paper we give a unified and short proof for the above mentioned classical results. 相似文献
8.
Benjamin J. Wyser 《Journal of Algebraic Combinatorics》2016,43(3):495-519
9.
Alexander Kreuzer 《Geometriae Dedicata》1994,53(2):163-186
It is well known that every locally projective linear space (M,M) with dimM 3, fulfilling the Bundle Theorem (B) can be embedded in a projective space. We give here a new construction for the projective embedding of linear spaces which need not be locally projective. Essentially for this new construction are the assumptions (A) and (C) that for any two bundles there are two points on every line which are incident with a line of each of these bundles. With the Embedding Theorem (7.4) of this note for example a [0,m]-space can be embedded in a projective space. 相似文献
10.
Peter Hohler 《Journal of Geometry》1972,2(2):161-174
A set of n-1 mutually orthogonal Latin squares of order n is a model of an affine plane with exactly n points on a line and every affine plane with n points on a line can be represented by n-1 mutually orthogonal Latin squares ([1]). In this paper we investigate properties of finite planes through the complete set of mutually orthogonal Latin squares representing the plane and mainly — vice versa — properties of the squares representing a fixed plane. The results are based on the geometrical configurations which hold in the planes. For presumed definitions and theorems which are not specially referred to see [4], [7], [3] or [6]. 相似文献
11.
Alan Rahilly 《Geometriae Dedicata》1982,13(2):173-194
The existence of Baer collineations in a projective plane is related to the existence of desargues-like configurations. The plane of order four is characterized as the only finite plane that possesses a Baer subplane partition into tangentially transitive Baer subplanes which is preserved by each of the tangentially transitive groups. It is shown that a finite projective plane has either no or one tangentially transitive Baer subplane or is partially transitive of Hughes type (4, m), (5, m) or (6, m) for some m. The Lenz-Barlotti classes which contain a finite plane which is not a translation plane nor its dual and which possesses a tangentially transitive Baer subplane are shown to be classes I.1 and II.1. 相似文献
12.
Paola De Vito Eva Ferrara Dentice Pia Maria Lo Re Klaus Metsch 《Journal of Geometry》1999,64(1-2):67-79
It is known that a linear spaces of dimensiond has at least as many hyperplanes as points with equality if it is a (possibly degenerate) projective space. If there are only a few more hyperplanes than points, then the linear space can still be embedded in a projective space of the same dimension. But even if the difference between the number of hyperplanes and points is too big to ensure an embedding, it seems likely that the linear space is closely related to a projective space. We shall demonstrate this in the cased=4. 相似文献
13.
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
14.
Klaus Metsch 《Journal of Geometry》1990,37(1-2):128-141
We classify all finite linear spaces without three mutually parallel lines. Apart from two exceptions, such a space is necessarily a generalized projective plane, a simple extension of a generalized projective plane, or a complete inflated affine plane with a generalized projective plane at infinity.Dedicated to Giuseppe Tallini on the occasion of his 60th birthday 相似文献
15.
Keith E. Mellinger 《Designs, Codes and Cryptography》2003,30(1):63-71
By Andrè theory, it is well known how to algebraically convert a spread in a projective space to an equivalent spread (representing the same translation plane) in a projective space of different dimension and of different order (corresponding to a subfield of the kernel). The goal of this paper is to establish a geometric connection between any two such equivalent spreads by embedding them as subspaces and subgeometries of an ambient projective spaces. The connection can be viewed as a generalization of a construction due to Hirschfeld and Thas. 相似文献
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17.
Dirk Keppens 《Results in Mathematics》1987,12(3-4):297-324
The study of polarities in finite projective Hjelmslev spaces started with [5] where the plane 2-uniform case was treated. The results obtained there have been extended in [6] to the plane k-uniform case (k≧2). The present paper deals with polarities in the k-uniform n-dimensional PH-space PH(n,GF(q) [t] /tk)(k≧2, n≧2) with q odd. 相似文献
18.
Sharad S. Sane 《Journal of Geometry》1980,15(1):64-73
Associated with every finite projective Hjelmslev plane is an invariant pair (t,r): t is the number of neighbours of a given point on a given line passing through it and r is the order of the underlying projective plane. The Drake-Lenz method [2],[3] of using auxiliary matrices for the constructions of projective Hjelmslev planes has become standard by now. This paper is intended to give some new constructions of projective Hjelmslev planes with invariant pairs (t,3) by making use of the generalization and improvement of the Drake-Lenz theorem [3] obtained by the author in [6] and [7]. The results of this paper add 8 new values to the list ([5], example 3.7(ii)) of invariant pairs (t,3) with t 1,000 for projective Hjelmslev planes. 相似文献
19.
Motivated by the works of Ngo and Du [H. Ngo, D. Du, A survey on combinatorial group testing algorithms with applications to DNA library screening, DIMACS Series in Discrete Mathematics and Theoretical Computer Science 55 (2000) 171–182], the notion of pooling spaces was introduced [T. Huang, C. Weng, Pooling spaces and non-adaptive pooling designs, Discrete Mathematics 282 (2004) 163–169] for a systematic way of constructing pooling designs; note that geometric lattices are among pooling spaces. This paper attempts to draw possible connections from finite geometry and distance regular graphs to pooling spaces: including the projective spaces, the affine spaces, the attenuated spaces, and a few families of geometric lattices associated with the orbits of subspaces under finite classical groups, and associated with d-bounded distance-regular graphs. 相似文献
20.
MohammadHossein Bateni Erik D. Demaine MohammadTaghi Hajiaghayi Mohammad Moharrami 《Discrete and Computational Geometry》2007,38(3):615-637
Embedding metrics into constant-dimensional geometric spaces, such as the Euclidean plane, is relatively poorly understood.
Motivated by applications in visualization, ad-hoc networks, and molecular reconstruction, we consider the natural problem
of embedding shortest-path metrics of unweighted planar graphs (planar graph metrics) into the Euclidean plane. It is known
that, in the special case of shortest-path metrics of trees, embedding into the plane requires
distortion in the worst case [M1], [BMMV], and surprisingly, this worst-case upper bound provides the best known approximation
algorithm for minimizing distortion. We answer an open question posed in this work and highlighted by Matousek [M3] by proving
that some planar graph metrics require
distortion in any embedding into the plane, proving the first separation between these two types of graph metrics. We also
prove that some planar graph metrics require
distortion in any crossing-free straight-line embedding into the plane, suggesting a separation between low-distortion plane
embedding and the well-studied notion of crossing-free straight-line planar drawings. Finally, on the upper-bound side,
we prove that all outerplanar graph metrics can be embedded into the plane with
distortion, generalizing the previous results on trees (both the worst-case bound and the approximation algorithm) and building
techniques for handling cycles in plane embeddings of graph metrics. 相似文献