论文标题
平衡挤压复合体
Balanced squeezed Complexes
论文作者
论文摘要
考虑到任何订单的理想$ u $由颜色平方的单元组成，涉及带有$ d $颜色的变量，我们将其与平衡的$（d-1）$ - 尺寸 - 尺寸简单复杂的$δ_ {\ mathrm {bal}}}（u）$，我们称之为平衡的squeeezed squeezed complect。实际上，这些复合物具有类似于Kalai引入的挤压球和作者引入的更一般挤压复合物的特性。我们表明，任何平衡的挤压复合物都是顶点解释的，并且可以从基础订单理想中读取其标志$ h $ -vector。此外，我们明确描述其stanley-reisner理想$ i_ {δ_ {\ mathrm {bal}}}（u）} $。如果$ u $也发生了变化，我们确定$ i_ {δ_{\ mathrm {bal}}（u）} $的多层的通用初始理想，并确定平衡的挤压复杂的$δ_{\ mathrm {bal}}（bal}}}}（u）$具有相同的逐渐相同的数量，可以从complect of Complect colders-shift。我们还介绍了一类无色平方的单样理想，这些理想可能被视为对经典无方稳定稳定的单样理想的概括，并表明可以从最小的发电机中读取其分级的贝蒂数字。此外，我们开发了一些用于计算分级Betti数字的工具。
Given any order ideal $U$ consisting of color-squarefree monomials involving variables with $d$ colors, we associate to it a balanced $(d-1)$-dimensional simplicial complex $Δ_{\mathrm{bal}}(U)$ that we call a balanced squeezed complex. In fact, these complexes have properties similar to squeezed balls as introduced by Kalai and the more general squeezed complexes, introduced by the authors. We show that any balanced squeezed complex is vertex-decomposable and that its flag $h$-vector can be read off from the underlying order ideal. Moreover, we describe explicitly its Stanley-Reisner ideal $I_{Δ_{\mathrm{bal}}(U)}$. If $U$ is also shifted, we determine the multigraded generic initial ideal of $I_{Δ_{\mathrm{bal}}(U)}$ and establish that the balanced squeezed complex $Δ_{\mathrm{bal}}(U)$ has the same graded Betti numbers as the complex obtained from color-shifting it. We also introduce a class of color-squarefree monomial ideals that may be viewed as a generalization of the classical squarefree stable monomial ideals and show that their graded Betti numbers can be read off from their minimal generators. Moreover, we develop some tools for computing graded Betti numbers.
