共查询到20条相似文献,搜索用时 15 毫秒
1.
Antonino Giorgio Spera 《Journal of Geometry》1991,40(1-2):175-185
We prove that a translation divisible design (TDD) with an abelian translation group can be embedded in PG (n,q) for some n2. Moreover we study affine TDD's showing that they have an (elementary) abelian translation group. A construction for TDD's with an abelian translation group which are not affine is given too. 相似文献
2.
Starting from desarguesian and twisted field planes we construct and study some classes of divisible designs admitting an automorphism group which is 2-transitive on the set of point classes. 相似文献
3.
4.
Antonino Giorgio Spera 《Journal of Geometry》1996,57(1-2):177-190
We construct some classes of -near-symmetric divisible designs by permutation group methods. We also define and study Paley divisible designs which generalize the well-known class of Paley 2-designs.Dedicated to professor Giuseppe Tallini 相似文献
5.
By removing the components of at-spread
of a finite projective spacePG(d, q) from each hyperplane ofPG(d, q), the blocks of a regular group divisible design
are obtained We characterize geometrict-spreads as thoset-spreads
which are such that the dual of
is also a group divisible design. 相似文献
6.
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
7.
Hiroki Tamura 《组合设计杂志》2006,14(6):451-462
We obtain new conditions on the existence of a square matrix whose Gram matrix has a block structure with certain properties, including D‐optimal designs of order , and investigate relations to group divisible designs. We also find a matrix with large determinant for n = 39. © 2006 Wiley Periodicals, Inc. J Combin Designs 14: 451–462, 2006 相似文献
8.
Antonino Giorgio Spera 《Geometriae Dedicata》1992,42(3):285-294
We study and characterize semi-regular (s, k, λ1, λ2)-divisible designs which admit a Frobenius group as their translation group. Moreover, we give a construction method for
such designs by generalized admissible triads. 相似文献
9.
James A. Davis 《Discrete Mathematics》1993,120(1-3):261-268
A construction is given for a (p2a(p+1),p2,p2a+1(p+1),p2a+1,p2a(p+1)) (p a prime) divisible difference set in the group H×Z2pa+1 where H is any abelian group of order p+1. This can be used to generate a symmetric semi-regular divisible design; this is a new set of parameters for λ1≠0, and those are fairly rare. We also give a construction for a (pa−1+pa−2+…+p+2,pa+2, pa(pa+pa−1+…+p+1), pa(pa−1+…+p+1), pa−1(pa+…+p2+2)) divisible difference set in the group H×Zp2×Zap. This is another new set of parameters, and it corresponds to a symmetric regular divisible design. For p=2, these parameters have λ1=λ2, and this corresponds to the parameters for the ordinary Menon difference sets. 相似文献
10.
M. S. Sgibnev 《Mathematical Notes》1989,46(4):794-798
Translated from Matematicheskie Zametki, Vol. 46, No. 4, pp. 60–65, October, 1989. 相似文献
11.
12.
Dieter Jungnickel 《Journal of Geometry》1980,15(2):153-157
We consider square divisible designs with parameters n, m, k=r, 0 and . We show that being disjoint induces an equivalence relation on the block set of such a design and that any two disjoint blocks meet precisely the same point classes. Also, the intersection number of two blocks depends only on their equivalence classes. The number of blocks disjoint with a given block is at most n–1; equality holds for all blocks iff the dual of the given design is also divisible with the same parameters. We then give a few applications.The author gratefully acknowledges the support of the Deutsche Forschungsgemeinschaft via a Heisenberg grant during the time of this research. 相似文献
13.
14.
Kishore Sinha Sanpei Kageyama 《Annals of the Institute of Statistical Mathematics》1989,41(2):409-414
Two new methods of constructing group divisible designs are given. In particular, a new resolvable solution for the SR 39 is presented. 相似文献
15.
16.
17.
I. Sh. o. Aliev 《Siberian Mathematical Journal》1972,13(3):341-348
18.
Lijun Ji 《Designs, Codes and Cryptography》2018,86(10):2255-2260
For positive integers n, k with \(3\le k\le n\), let \(X=\mathbb {F}_{2^n}\setminus \{0,1\}\), \({\mathcal {G}}=\{\{x,x+1\}:x\in X\}\), and \({\mathcal {B}}_k=\left\{ \{x_1,x_2,\ldots ,x_k\}\!\subset \!X:\sum \limits _{i=1}^kx_i=1,\ \sum \limits _{i\in I}x_i\!\ne \!1\ \mathrm{for\ any}\ \emptyset \!\ne \!I\!\subsetneqq \!\{1,2,\ldots ,k\}\right\} \). Lee et al. used the inclusion–exclusion principle to show that the triple \((X,{\mathcal {G}},{\mathcal {B}}_k)\) is a \((k,\lambda _k)\)-GDD of type \(2^{2^{n-1}-1}\) for \(k\in \{3,4,5,6,7\}\) where \(\lambda _k=\frac{\prod _{i=3}^{k-1}(2^n-2^i)}{(k-2)!}\) (Lee et al. in Des Codes Cryptogr, https://doi.org/10.1007/s10623-017-0395-8, 2017). They conjectured that \((X,{\mathcal {G}},{\mathcal {B}}_k)\) is also a \((k,\lambda _k)\)-GDD of type \(2^{2^{n-1}-1}\) for any integer \(k\ge 8\). In this paper, we use a similar construction and counting principles to show that there is a \((k,\lambda _k)\)-GDD of type \((q^2-q)^{(q^{n-1}-1)/(q-1)}\) for any prime power q and any integers k, n with \(3\le k\le n\) where \(\lambda _k=\frac{\prod _{i=3}^{k-1}(q^n-q^i)}{(k-2)!}\). Consequently, their conjecture holds. Such a method is also generalized to yield a \((k,\lambda _k)\)-GDD of type \((q^{\ell +1}-q^{\ell })^{(q^{n-\ell }-1)/(q-1)}\) where \(\lambda _k=\frac{\prod _{i=3}^{k-1}(q^n-q^{\ell +i-1})}{(k-2)!}\) and \(k+\ell \le n+1\). 相似文献
19.
Willem Mielants 《Journal of Geometry》1979,12(2):89-98
Many non-existence theorems are known for symmetric group divisible partial designs. In the case that these partial designs are auto-dual with
1=0, an ideal incidence structure can be defined whose elements are the equivalence-classes of non-collinear points and parallel blocks. Except for some trivial cases this incidence structure turns out to be a symmetric design, and by studying its existence we can prove much more powerful non-existence theorems. 相似文献
20.
We introduce the concept of linked systems of symmetric group divisible designs. The connection with association schemes is established, and as a consequence we obtain an upper bound on the number of symmetric group divisible designs which are linked. Several examples of linked systems of symmetric group divisible designs are provided. 相似文献