论文标题
$ det^{s^2} $ map的存在
Existence of the $det^{S^2}$ map
论文作者
论文摘要
在本文中，我们表明，对于矢量空间$ v_d $ dimension $ d $的存在是线性映射$ det^{s^2}：v_d^{\ otimes d（2d-1）} \ to k $ to k $ to k $ to t to属性，该属性是$ det^{s^2}（s^2}（\ otimes__^1 \ leq iq iq iq iq iq iq iq iq iq iq iq iq iq iq iq iq iq iq iq iq iq iq 2d}}如果存在$ 1 \ leq x <y <z \ leq 2d $，这样$ v_ {x，y} = v_ {x，z} = v_ {y，z} $。在[4]中猜想了这种图的存在。我们将地图$ det^{s^2} $的两个应用程序介绍给几何和组合。
In this paper we show that for a vector space $V_d$ of dimension $d$ there exists a linear map $det^{S^2}:V_d^{\otimes d(2d-1)}\to k$ with the property that $det^{S^2}(\otimes_{1\leq i<j\leq 2d}(v_{i,j}))=0$ if there exists $1\leq x<y<z\leq 2d$ such that $v_{x,y}=v_{x,z}=v_{y,z}$. The existence of such a map was conjectured in [4]. We present two applications of the map $det^{S^2}$ to geometry and combinatorics.
