共查询到20条相似文献,搜索用时 31 毫秒
1.
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
2.
The concept of projective lattice geometry generalizes the classical synthetic concept of projective geometry, including projective geometry of modules.In this article we introduce and investigate certain structure preserving mappings between projective lattice geometries. Examples of these so-calledprojective mappings are given by isomorphisms and projections; furthermore all linear mappings between modules induce projective mappings between the corresponding projective geometries. 相似文献
3.
We introduce the notion of a convex geometry extending the notion of a finite closure system with the anti-exchange property known in combinatorics. This notion becomes essential for the different embedding results in the class of join-semidistributive lattices. In particular, we prove that every finite join-semidistributive lattice can be embedded into a lattice SP(A) of algebraic subsets of a suitable algebraic lattice A. This latter construction, SP(A), is a key example of a convex geometry that plays an analogous role in hierarchy of join-semidistributive lattices as a lattice of equivalence relations does in the class of modular lattices. We give numerous examples of convex geometries that emerge in different branches of mathematics from geometry to graph theory. We also discuss the introduced notion of a strong convex geometry that might promise the development of rich structural theory of convex geometries. 相似文献
4.
5.
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
6.
If V is a variety of lattices and L a free lattice in V on uncountably many generators, then any cofinal sublattice of L generates all of V. On the other hand, any modular lattice without chains of order-type +1 has a cofinal distributive sublattice. More generally, if a modular lattice L has a distributive sublattice which is cofinal modulo intervals with ACC, this may be enlarged to a cofinal distributive sublattice. Examples are given showing that these existence results are sharp in several ways. Some similar results and questions on existence of cofinal sublattices with DCC are noted.This work was done while the first author was partly supported by NSF contract MCS 82-02632, and the second author by an NSF Graduate Fellowship. 相似文献
7.
Marcus Greferath 《Geometriae Dedicata》1996,60(2):219-224
Free left modules over right Bezout domains are characterized by a set of geometric axioms resembling those of U. Brehm, where results of this kind have been obtained for torsion-free left modules over left Ore domains. Discourses by S. E. Schmidt and the present author have come to similar results for other classes of rings and modules.The author would like to thank Mrs Juliane Plachta, Mrs Heidrun Wenzel and the referee for helpful comments in language and style. 相似文献
8.
We describe the free modular lattice generated by two chains and a single point, under the assumption that there are few meets.
Received February 11, 2005; accepted in final form August 11, 2005. 相似文献
9.
We develop a representation theory for convex geometries and meet distributive lattices in the spirit of Birkhoff's theorem characterizing distributive lattices. The results imply that every convex geometry on a set X has a canonical representation as a poset labelled by elements of X. These results are related to recent work of Korte and Lovász on antimatroids. We also compute the convex dimension of a convex geometry.Supported in part by NSF grant no. DMS-8501948. 相似文献
10.
Projective geometry is formulated in the language of geometric algebra, a unified mathematical language based on Clifford algebra. This closes the gap between algebraic and synthetic approaches to projective geometry and facilitates connections with the rest of mathematics.This work was partially supported by NSF grant MSM-8645151. 相似文献
11.
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
12.
On the full automorphism group of a graph 总被引:11,自引:0,他引:11
C. D. Godsil 《Combinatorica》1981,1(3):243-256
While it is easy to characterize the graphs on which a given transitive permutation groupG acts, it is very difficult to characterize the graphsX with Aut (X)=G. We prove here that for the certain transitive permutation groups a simple necessary condition is also sufficient. As a corollary
we find that, whenG is ap-group with no homomorphism ontoZ
p
wrZ
p
, almost all Cayley graphs ofG have automorphism group isomorphic toG. 相似文献
13.
Simon Thomas 《Geometriae Dedicata》1996,63(3):247-253
Let
be a finite field, and let (, B) be a nontrivial 2-(n, k, 1)-design over
. Then each point induces a (k–1)-spread S on /. (, B) is said to be a geometric design if S is a geometric spread on / for each . In this paper, we prove that there are no geometric designs over any finite field
.Research partially supported by NSF grant DMS-8703229. 相似文献
14.
Jaroslav Ježek 《Order》1985,2(1):69-79
For any N3 there exists a lattice L isomorphic with NL (the free product of its own N copies) but not isomorphic with kL for any k–2,...,N-1. 相似文献
15.
Christian Herrmann 《Order》1991,8(3):275-281
For modular lattices of finite length, vector space representations are shown to give rise to contracted representations of homomorphic imagesDedicated to the memory of Alan Day 相似文献
16.
17.
We construct an innite family of (q + 1)-regular Ramanujan graphs
X
n
of girth 1. We also give
covering maps X
n+1
X
n
such that the minimal
common covering of all the X
n
s is the universal
covering tree. 相似文献
18.
A theorem of N. Terai and T. Hibi for finite distributive lattices and a theorem of Hibi for finite modular lattices (suggested by R.P. Stanley) are equivalent to the following: if a finite distributive or modular lattice of rank d contains a complemented rank 3 interval, then the lattice is (d+1)-connected.In this paper, the following generalization is proved: Let L be a (finite or infinite) semimodular lattice of rank d that is not a chain (d∈N0). Then the comparability graph of L is (d+1)-connected if and only if L has no simplicial elements, where z∈L is simplicial if the elements comparable to z form a chain. 相似文献
19.
The design of linear algebra and geometry 总被引:2,自引:0,他引:2
David Hestenes 《Acta Appl Math》1991,23(1):65-93
Conventional formulations of linear algebra do not do justice to the fundamental concepts of meet, join, and duality in projective geometry. This defect is corrected by introducing Clifford algebra into the foundations of linear algebra. There is a natural extension of linear transformations on a vector space to the associated Clifford algebra with a simple projective interpretation. This opens up new possibilities for coordinate-free computations in linear algebra. For example, the Jordan form for a linear transformation is shown to be equivalent to a canonical factorization of the unit pseudoscalar. This approach also reveals deep relations between the structure of the linear geometries, from projective to metrical, and the structure of Clifford algebras. This is apparent in a new relation between additive and multiplicative forms for intervals in the cross-ratio. Also, various factorizations of Clifford algebras into Clifford algebras of lower dimension are shown to have projective interpretations.As an important application with many uses in physics as well as in mathematics, the various representations of the conformal group in Clifford algebra are worked out in great detail. A new primitive generator of the conformal group is identified. 相似文献
20.
This paper reviews current work based on von Neumann's coordinization theorem. 相似文献