论文标题
无平方功率的归一化深度函数
The normalized depth function of squarefree powers
论文作者
论文摘要
引入了无方形理想的无平方幂的深度。令$ i $为多项式环$ s = k [x_1，\ ldots，x_n] $的单一理想。 $ k $ -th squarefree $ i^{[k] $ $ i $是$ s $的理想，这些$ s $由g（i）$ in g（i）$中的每个$ u_i \ in $ g（i）$是$ g（i）$是$ i $ $ i $ $ i $的独特的最小生成器系统。令$ d_k $表示属于$ g（i^{[k]}）$的最低单元。一个人具有$ \ operatatorName {depth}（s/i^{[k]}）\ geq d_k -1 $。设置$ g_i（k）= \ operatatorName {depth}（s/i^{[k]}） - （d_k -1）$，一个人调用$ i $的归一化深度函数$ g_i（k）$。计算体验强烈邀请我们提出这样的猜想，即归一化的深度功能是非渗透的。在本文中，深入研究了有限简单图的边缘理想的归一化深度功能。
The depth of squarefree powers of a squarefree monomial ideal is introduced. Let $I$ be a squarefree monomial ideal of the polynomial ring $S=K[x_1,\ldots,x_n]$. The $k$-th squarefree power $I^{[k]}$ of $I$ is the ideal of $S$ generated by those squarefree monomials $u_1\cdots u_k$ with each $u_i\in G(I)$, where $G(I)$ is the unique minimal system of monomial generators of $I$. Let $d_k$ denote the minimum degree of monomials belonging to $G(I^{[k]})$. One has $\operatorname{depth}(S/I^{[k]}) \geq d_k -1$. Setting $g_I(k) = \operatorname{depth}(S/I^{[k]}) - (d_k - 1)$, one calls $g_I(k)$ the normalized depth function of $I$. The computational experience strongly invites us to propose the conjecture that the normalized depth function is nonincreasing. In the present paper, especially the normalized depth function of the edge ideal of a finite simple graph is deeply studied.
