• 主题
高级搜索  >
历史搜索 清空历史
首页> 外文期刊>Designs, Codes and Crytography >The Quintic Grassmannian G_(1,4,2) in PG(9,2)
【24h】

The Quintic Grassmannian G_(1,4,2) in PG(9,2)

机译：PG（9,2）中的Quintic Grassmannian G_（1,4,2）

获取原文
获取原文并翻译 | 示例
           
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

The 155 points of the Grassmannian G_(1,4,2) of lines of PG(4,2) = PV(5,2) are those points x∈PG(9,2) = P(∧ ~2V(5,2)) which satisfy a certain quintic equation Q(x) = 0. (The quintic polynomial Q is given explicitly in Shaw and Gordon.) A projective flat X is contained in PG(9,2) will be termed odd or even according as X intersects G_(1,4,2) in an odd or even number of points. Let Q(x_1,...,x_5) denote the alternating quinquelinear form obtained by completely polarizing Q. We define the associate Y = X~# of a r-flat X is contained in PG(9,2) by Y = {y∈PG(n,2) | Q(x_1,x_2,x_3,x_4,y) = 0, for all x_1,x_2,x_3,x_4∈X}. Because Q is quinquelinear, the associate X~# of an r-flat X is an s-flat for some s. The cases where r = 4 are of particular interest: if X is an odd 4-flat then X is contained in X~# while if X is an even 4-flat then X~# is necessarily also a 4-flat which is moreover disjoint from X. We give an example of an odd 4-flat X which is self-associate: X~# = X. An example of an even 4-flat X such that (X~#)~# = X is provided by any 4-flat X which is external to G_(1,4,2)- However, it appears that the two possibilities just illustrated, namely X~# = X for an odd 4-flat and (X~#)~# = X for an even 4-flat, are the exception rather than the rule. Indeed, we provide examples of odd 4-flats for which X~# = PG(9,2) and of even 4-flats for which X~(###) = X.
机译：PG（4,2）= PV（5,2）的直线的Grassmannian G_（1,4,2）的155个点是那些点x∈PG（9,2）= P（∧〜2V（5， 2））满足某个五次方程Q（x）=0。（在Shaw和Gordon中明确给出了五次多项式Q。）PG（9,2）中包含的射影平面X将被称为奇数或偶数因为X在奇数或偶数点与G_（1,4,2）相交。令Q（x_1，...，x_5）表示通过完全极化Q获得的交替五重线性形式。我们定义PG（9,2）中包含的r-flat X的关联Y = X〜 y∈PG（n，2）|对于所有x_1，x_2，x_3，x_4∈X}，Q（x_1，x_2，x_3，x_4，y）= 0。因为Q是五重线性的，所以r平面X的伴随X_＃对于某些s是s平面。 r = 4的情况特别令人感兴趣：如果X是奇数4进制，则X包含在X〜＃中，而如果X是偶数4进制，那么X〜＃也必然是4进制，而且与X不相交。我们给出一个自相关的奇数4-flat X的示例：X〜＃=X。一个等式4-flat X的示例，使得（X〜＃）〜＃= X由G_（1,4,2）外部的任何4-flat X-但是，似乎刚刚说明了两种可能性，即X〜＃= X表示奇数4-flat和（X〜＃）〜＃= X为偶数4位数，是例外而不是规则。确实，我们提供了X〜＃= PG（9,2）的奇数4-flats和X〜（###）= X的偶数4-flats的示例。

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号