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111.
A Mendelsohn triple system (MTS) corresponds to an idempotent semisymmetric Latin square (quasigroup) of the same order. A holey MTS is called frame self-orthogonal, briefly FSOMTS, if its associated holey semisymmetric Latin square is frame self-orthogonal. In this paper, we use FSOMTS(hn) to denote an FSOMTS with n spanning holes of size h. The existence of FSOMTS(hn) for h3 has been known with a few exceptions. We extend the existing results and determine the necessary and sufficient conditions for the existence of FSOMTS(hn) for any h and n with some possible exceptions. 相似文献
112.
There exist few examples of negative Latin square type partial difference sets (NLST PDSs) in nonabelian groups. We present a list of 176 inequivalent NLST PDSs in 48 nonisomorphic, nonabelian groups of order 64. These NLST PDSs form 8 nonisomorphic strongly regular graphs. These PDSs were constructed using a combination of theoretical techniques and computer search, both of which are described. The search was run exhaustively on 212/267 nonisomorphic groups of order 64. 相似文献
113.
114.
遗传算法作为一种随机化优化搜索方法,已经在很多领域得到了成功应用,但其存在控制参数多且配置困难的问题.本文采用一类最新试验设计方法-计算机试验设计,对遗传算法的参数配置进行优化.结果表明,基于正交拉丁超立方设计的参数配置,其算法的计算精度和速度表现最佳.模拟结果进一步讨论了不同试验设计方案在遗传算法中的差别. 相似文献
115.
最佳拉丁方与高级原幻方 总被引:1,自引:0,他引:1
本文证明了 (n ,2 ) =(n ,3) =1时 ,有n阶的正交的最佳拉丁方。若n =4k ,或n是个不为 3的奇数 ,则有n阶的正交的高级原幻方 相似文献
116.
In this paper, two new direct construction methods are given for holey self‐orthogonal Latin squares with a symmetric orthogonal mate (HSOLSSOMs). Some new HSOLSSOMs using already known methods are also given. The known existence results for HSOLSSOMs of types 1m u1 and hn are improved; for type 1m u1 there remain just four possible exceptions with u odd and 3 ≤ u ≤ 15; for type hn, there are just two possible exceptions remaining, for (h, n) = (6, 12) and (6, 18). As a byproduct, the known existence results for three holey mutually orthogonal Latin squares (3 HMOLS) are also improved. © 2001 John Wiley & Sons, Inc. J Combin Designs 9: 435–444, 2001 相似文献
117.
The teleportation of an arbitrary n-particle state is proposed
when n pairs of entangled particles are utilized as quantum
channels. It can be successfully realized with a certain
probability which is determined by the smallest coefficients of n
entangled pairs. Using a Latin square of order 2n, explicit
expressions of two unitary operations corresponding to different
Bell-basis measurements performed by Alice can be obtained at the
end of Bob. 相似文献
118.
Nicholas Cavenagh 《Journal of Combinatorial Theory, Series A》2008,115(1):193-197
Given a pair of Latin squares, we may remove from both squares those cells that contain the same symbol in corresponding positions. The resulting pair T={P1,P2} of partial Latin squares is called a Latin bitrade. The number of filled cells in P1 is called the size of T. There are at least two natural ways to define the genus of a Latin bitrade; the bitrades of genus 0 are called spherical. We construct a simple bijection between the isomorphism classes of planar Eulerian triangulations on v vertices and the main classes of spherical Latin bitrades of size v−2. Since there exists a fast algorithm (due to Batagelj, Brinkmann and McKay) for generating planar Eulerian triangulations up to isomorphism, our result implies that also spherical Latin bitrades can be generated very efficiently. 相似文献
119.
如果2个n阶不完全拉丁方重叠后正好产生r个不同的有序对,则称它们是,r-正交的,记作r—IMOLS(n,u),其中u为缺少的子拉丁方的阶数.进一步,如果第2个拉丁方是第1个拉丁方的转置,则称它们是,r-自正交的,记作r—ISOLS(n,u).本文给出当u∈{1,2,3,4}时,r—ISOLS(4m+u,u)的存在性. 相似文献
120.