Orlik-Solomon型代数中的Groebner基和对角基
Groebner and diagonal bases in Orlik-Solomon type algebras
摘要：
拟阵M的Orlik-Solomon代数是拟阵的圈的边界所生成的理想I（M）在点上的外代数的商。复拟阵的Orlik-Solomon代数与复超平面排列的补的上同调之间存在同构。在这篇文章中，Orlik-Solomon代数的推广，称为X-代数，被认为是。这些新代数除了Orlik-Solomon代数外，还包括向量集的Orlik-Solomon-Terao代数和定向拟阵的Cordovil代数。为了对Orlik-Solomon-Terao代数的“无断路基”的一个重要性质进行编码，Andras Szenes引入了一种特殊类型的基，即所谓的“对角基”。这个概念自然地延伸到X-代数。本文综述了作者关于I（M）的Groebner基和Orlik-Solomon型代数的对角基的构造所得到的结果，并给出了Szenes引入的一个"迭代剩余公式“的组合模拟.
英文摘要：
The Orlik-Solomon algebra of a matroid M is the quotient of the exterior algebra on the points by the ideal I(M) generated by the boundaries of the circuits of the matroid. There is an isomorphism between the Orlik-Solomon algebra of a complex matroid and the cohomology of the complement of a complex arrangement of hyperplanes. In this article a generalization of the Orlik-Solomon algebras, called X-algebras, are considered. These new algebras include, apart from the Orlik-Solomon algebras, the Orlik-Solomon-Terao algebra of a set of vectors and the Cordovil algebra of an oriented matroid. To encode an important property of the "no broken circuit bases" of the Orlik-Solomon-Terao algebras, Andras Szenes has introduced a particular type of bases, the so called "diagonal bases". This notion extends naturally to X-algebras. We give a survey of the results obtained by the authors concerning the construction of Groebner bases of I(M) and diagonal bases of Orlik-Solomon type algebras and we present the combinatorial analogue of an ``iterative residue formula'' introduced by Szenes.
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