论文标题
超图LSS-理想和对称张量的坐标部分
Hypergraph LSS-ideals and coordinate sections of symmetric tensors
论文作者
论文摘要
令k为一个字段，[n] = {1，...，n}，h =（[n]，e）成为超图。对于整数d> = 1，k [y_ {y_ {ij}〜：〜：〜（i，j）\ in [n] x [d] in [y_ {ij}〜： H。 s_ {n，k}^d均值k对称张量的n变量<= d <= d，以得出其坐标部分的不可约性的结果。为此，我们提供了有关l_h^k（d）的原始属性和完整交点属性的结果。然后，我们使用HyperGraph H的阳性匹配分解的组合概念来提供何时l_h^k（d）变成prime的界限，以提供S_ {n，k}^d的坐标部分的不可约性的结果。
Let K be a field, [n]= {1,...,n} and H=([n],E) be a hypergraph. For an integer d >= 1 the Lovasz-Saks-Schrijver ideal (LSS-ideal) L_H^K (d) in K[y_{ij}~:~(i,j) \in [n] x [d]] is the ideal generated by the polynomials $f^{(d)}_{e}= \sum\limits_{j=1}^{d} \prod\limits_{i \in e} y_{ij}$ for edges e of H. In this paper for an algebraically closed field K and a k-uniform hypergraph H=([n],E) we employ a connection between LSS-ideals and coordinate sections of the closure of the set S_{n,k}^d of homogeneous degree k symmetric tensors in n variables of rank <= d to derive results on the irreducibility of its coordinate sections. To this end we provide results on primality and the complete intersection property of L_H^K (d). We then use the combinatorial concept of positive matching decomposition of a hypergraph H to provide bounds on when L_H^K(d) turns prime to provide results on the irreducibility of coordinate sections of S_{n, k}^d.
