标题： 构建具有固定贝蒂数的单项式理想 显示英文标题

标题： Building monomial ideals with fixed betti numbers

摘要： 鉴于理想生成元的数量增加会导致计算生成元之间关系的复杂性增加，本文识别出具有越来越多生成元的单项式理想的集合，这些理想具有可预测的自由分解。 我们使用离散同伦理论中的基本坍塌来构造无限多个单项式理想，这些理想具有任意数量的生成元，并且具有相似或相同的贝蒂数。 我们证明了在理想扩展过程中，每个非混合（纯）部分的科恩-麦克劳尔属性得到保持。 显示英文摘要

摘要： Motivated by the fact that as the number of generators of an ideal grows so does the complexity of calculating relations among the generators, this paper identifies collections of monomial ideals with a growing number of generators which have predictable free resolutions. We use elementary collapses from discrete homotopy theory to construct infinitely many monomial ideals, with an arbitrary number of generators, which have similar or the same betti numbers. We show that the Cohen-Macaulay property in each unmixed (pure) component of the ideal is preserved as the ideal is expanded.