论文标题
某些单一理想的力量发电机数量下降
Certain monomial ideals whose numbers of generators of powers descend
论文作者
论文摘要
本文研究了多项式环中单一理想能力的最小发电机的数量。对于单个变量中的单体理想$ i $，Eliahou，Herzog和Saem给出了较小的下限$μ（i^2）\ ge 9 $，用于$ i^2 $的最小发电机的数量，$ i^2 $，$μ（i）\ geq 6 $。最近，Gasanova构建了单一理想，因此对于任何正整数$ n $，$μ（i）>μ（i^n）$。参考它们，我们构建了一类单一理想，以便为任何正整数$ n $ $μ（i）>μ（i^2）> \ cdots>μ（i^n）=（n+1）^2 $，它提供了功能$μ（i^k）$的最出乎意料的行为之一。单一理想还提供了一个奇特的例子，使得$ r/i^n $ discends的Cohen-Macaulay类型（或不可约性索引）。
This paper studies the numbers of minimal generators of powers of monomial ideals in polynomial rings. For a monomial ideal $I$ in two variables, Eliahou, Herzog, and Saem gave a sharp lower bound $μ(I^2)\ge 9$ for the number of minimal generators of $I^2$ with $μ(I)\geq 6$. Recently, Gasanova constructed monomial ideals such that $μ(I)>μ(I^n)$ for any positive integer $n$. In reference to them, we construct a certain class of monomial ideals such that $μ(I)>μ(I^2)>\cdots >μ(I^n)=(n+1)^2$ for any positive integer $n$, which provides one of the most unexpected behaviors of the function $μ(I^k)$. The monomial ideals also give a peculiar example such that the Cohen-Macaulay type (or the index of irreducibility) of $R/I^n$ descends.
