In this article, we investigate the cardinality of Grobner basis under various orderings. We identify a family of polynomials F and a criteria for the monomial orderings such that the reduced Grobner basis is double exponential in cardinality. We also show that the said criteria is satisfied by orderings such as lexicographic, degree lexicographic and weighted orderings.

翻译：本文研究了不同序下Gröbner基的基数。我们确定了一族多项式F以及单项式序的一个判据，使得约化Gröbner基具有双重指数级的基数。我们还证明了该判据可由诸如字典序、度字典序及加权序等序所满足。