标题： 边理想具有线性商的幂 显示英文标题

标题： Powers of Edge Ideals with Linear Quotients

摘要： 我们证明了反向圈的边理想的所有二次及更高次幂具有线性商序，尽管这些边理想本身并不具备此性质，从而以肯定的方式解决了霍费尔和惠尔登提出的一个公开问题，并提供了第一类间隙自由图，其边理想的幂满足这一性质。 我们还为任意具有线性商的二次单式理想的所有幂构造了一个显式且直观的线性商序。这扩展了一个赫兹格、希比和郑广为人知的结果。 作为结果，我们给出了胡须图的边理想的投射维数和Betti数的显式公式。 显示英文摘要

摘要： We prove that second and higher powers of the edge ideals of anticycles admit linear quotient orderings, although the edge ideals themselves do not, thus resolving an open question of Hoefel and Whieldon in the affirmative and providing the first class of gap-free graphs whose edge ideals satisfy this property on their powers. We also construct an explicit and straightforward linear quotient ordering for any power of a quadratic monomial ideal which admits linear quotients. This expands on a well-known result of Herzog, Hibi, and Zheng. As a consequence, we give explicit formulas for the projective dimension and Betti numbers of the edge ideals of whisker graphs.