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1.
The aim of this paper is to present a construction of t-divisible designs (DDs) for t > 3, because such DDs seem to be missing in the literature. To this end, tools such as finite projective spaces and their algebraic varieties are employed. More precisely, in a first step an abstract construction, called t-lifting, is developed. It starts from a set X containing a t-DD and a group G acting on X. Then several explicit examples are given, where X is a subset of PG(n,q) and G is a subgroup of GL_n + 1(q). In some cases X is obtained from a cone with a Veronesean or an h-sphere as its basis. In other examples, X arises from a projective embedding of a Witt design. As a result, for any integer t ≥ 2 infinitely many non-isomorphic t-DDs are found.Dedicated to Walter Benz on the occasion of his 75th birthday. 相似文献
2.
Many different divisible designs are already known. Some of them possess remarkable automorphism groups, so called dual translation groups. The existence of such an automorphism group enables us to characterize its associated divisible design as being isomorphic
to a substructure of a finite affine space.
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《Discrete Mathematics》2021,344(12):112623
In this paper, we construct two new symmetric designs with parameters 2- as designs invariant under certain subgroups of the full automorphism group of the Higman design. One is self-dual and has the full automorphism group of order 11520 and the other one is not self-dual and has the full automorphism group of order 2520. 相似文献
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The generalized chain geometry over the local ring $K(\varepsilon ; \sigma)The generalized chain geometry over the local ring of twisted dual numbers, where K is a finite field, is interpreted as a divisible design obtained from an imprimitive group action. Its combinatorial properties
as well as a geometric model in 4-space are investigated.
Dedicated to Helmut M?urer on the occasion of his 70th birthday 相似文献
6.
A resolvable modified group divisible design (RMGDD) is an MGDD whose blocks can be partitioned into parallel classes. In this article, we investigate the existence of RMGDDs with block size three and show that the necessary conditions are also sufficient with two exceptions. © 2005 Wiley Periodicals, Inc. J Combin Designs 15: 2–14, 2007 相似文献
7.
B.A.F. Wehrfritz 《Central European Journal of Mathematics》2009,7(3):387-394
We consider the existence or otherwise of canonical divisible normal subgroups of groups in general. We present more counterexamples
than positive results. These counterexamples constitute the substantive part of this paper.
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8.
Group divisible designs (GDDs) with block size 4 and at most 30 points are known for all feasible group types except three, namely , and . In this paper we provide solutions for the first two of these three 4‐GDDs without assuming any automorphisms. We also construct several other 4‐GDDs. These include classes of 4‐GDDs of types for where and solutions for 4‐GDDs of types for a wide range of values of satisfying or , including all cases with . Most of the remaining unknown 4‐GDDs of type have . 相似文献
9.
Li-dong Wang Hai-rong Kong Hong-juan Liu Department of Basic Courses Chinese People’s Armed Police Force Academy Langfang China School of Science Hebei University of Technology Tianjin China Department of Computer Science Engineering Langfang Polytechnic Institute China 《应用数学学报(英文版)》2011,27(3):407-418
In this paper, we investigate the existence of incomplete group divisible designs (IGDDs) with block size four, group-type (g, h) u and general index λ. The necessary conditions for the existence of such a design are that u ≥ 4, g ≥ 3h, λg(u 1) ≡ 0 (mod 3), λ(g h)(u 1) ≡ 0 (mod 3), and λu(u 1)(g 2 h 2 ) ≡ 0 (mod 12). These necessary conditions are shown to be sufficient for all λ≥ 2. The known existence result for λ = 1 is also improved. 相似文献
10.
Let x:M → Rn be an umbilical free hypersurface with non-zero principal curvatures.Then x is associated with a Laguerre metric g,a Laguerre tensor L,a Laguerre form C,and a Laguerre second fundamental form B,which are invariants of x under Laguerre transformation group.An eigenvalue of Laguerre tensor L of x is called a Laguerre eigenvalue of x.In this paper,we classify all oriented hypersurfaces with constant Laguerre eigenvalues and vanishing Laguerre form. 相似文献
11.
A pentagonal geometry PENT() is a partial linear space, where every line is incident with points, every point is incident with lines, and for each point , there is a line incident with precisely those points that are not collinear with . Here we generalize the concept by allowing the points not collinear with to form the point set of a Steiner system whose blocks are lines of the geometry. 相似文献
12.
Snigdha Banerjee Sanpei Kageyama Bhagwandas 《Annals of the Institute of Statistical Mathematics》1987,39(1):671-679
Summary Two-associate class PBIB designs, having association schemes of GD orL
2 types, are constructed by using patterned matrices and by methods of taking unions of sets of blocks. 相似文献
13.
《组合设计杂志》2018,26(11):519-539
Building upon the work of Wei and Ge (Designs, Codes, and Cryptography 74, 2015), we extend the range of positive integer parameters g, u, and m for which group divisible designs with block size 4 and type are known to exist. In particular, we show that the necessary conditions for the existence of these designs when and are sufficient in the following cases: , with one exception, 2651, , and . 相似文献
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Shakti Banerjee Bhagwandas S. Kageyama 《Annals of the Institute of Statistical Mathematics》1985,37(1):145-150
Summary Constructions of three series of regular GD and semi-regular GD designs are given. Furthermore, a series of rectangular PBIB
designs is constructed and particular cases of this series which reduce to PBIB designs with two associate classes are also
provided.
Written while visiting Department of Statistics, University of Indore, India, December 1983 through February 1984. 相似文献
15.
We determine a necessary and sufficient condition for the existence of semicyclic holey group divisible designs with block size three and group type . New recursive constructions on semicyclic incomplete holey group divisible designs are introduced to settle this problem completely. 相似文献
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N. S. Mendelsohn 《组合设计杂志》2006,14(6):415-422
Constructions are given for the production of symmetric block designs whose point set is divisible (partitionable) in several ways. Some properties of the dual design are also considered. © 2006 Wiley Periodicals, Inc. J Combin Designs 14: 415–422, 2006 相似文献
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A. D. Forbes 《组合设计杂志》2019,27(5):311-349
We show that the necessary conditions for the existence of group divisible designs with block size four (4‐GDDs) of type are sufficient for (mod ), = 39, 51, 57, 69, 87, 93, 111, 123 and 129, and for = 13, 17, 19, 23, 25, 29, 31 and 35. More generally, we show that for (mod 6), the possible exceptions occur only when , and there are no exceptions at all if has a divisor such that (mod 4) or is a prime not greater than 43. Hence, there are no exceptions when (mod 12). Consequently, we are able to extend the known spectrum for and 5 (mod 6). Also, we complete the spectrum for 4‐GDDs of type . 相似文献
19.
In this paper, we establish the existence of some infinite families of 2‐designs from ‐dimensional projective geometry , which admit ‐dimensional projective special linear group as their flag‐transitive automorphism group. 相似文献
20.
Dean Crnković B.G. Rodrigues Sanja Rukavina Vladimir D. Tonchev 《Discrete Mathematics》2017,340(10):2472-2478
This paper completes the enumeration of quasi-symmetric 2- designs supported by the dual code of the binary linear code spanned by the lines of , initiated in Rodrigues and Tonchev (2015). It is shown that supports exactly 30,264 nonisomorphic quasi-symmetric 2- designs. The automorphism groups of the related strongly regular graphs are computed. 相似文献