对组合数学在交换代数中的贡献。(ph-d论文）
Contribution in combinatorics in commutative algebra.(ph-d thesis)
摘要：
在第一章中，我们给出了Borel型单项理想的相关结果。另外，我们引入了一类新的单项式理想，称为$\de$ -不动理想，它推广了$p$ -Borel理想类，并将一些结果推广到这个新的理想类.在第二章中，我们计算了嵌入维数为3且具有强Lefschetz性质的完全交理想的逆字典序的通有初始理想，并证明了它是几乎逆字典序理想。这使我们能够在$n=3$和特征零的情况下给出Moreno猜想的一个证明.此外，我们证明了$d$ -组件的通用初始理想，相对于反向字典顺序，理想所产生的一个正则序列的齐次多项式的程度$d$是revlex，在一个特殊的，但重要的情况下。
英文摘要：
In the first chapter we present new results related on monomial ideals of Borel type. Also, we introduce a new class of monomial ideals, called $\de$-fixed ideals, which generalize the class of $p$-Borel ideals and we extend several results to this new class. In the second chapter, we compute the generic initial ideal, with repect to the reverse lexicographic order, of an ideal which define a complete intersection of embedding dimension three with strong Lefschetz property and we show that it is an almost reverse lexicographic ideal. This enable us to give a proof for Moreno's conjecture in the case $n=3$ and characteristic zero. Also, we prove that the $d$-component of the generic initial ideal, with respect to the reverse lexicographic order, of an ideal generated by a regular sequence of homogeneous polynomials of degree $d$ is revlex, in a particular, but important, case.
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