betti number meaning in English

贝蒂数
连通数

This article have two parts : g - fixed ideals and some ideas with stable betti numbers on shifting operations
本文分两部分： g -不变理想与移位运算下保持分次betti数不变的一些理想。
When i s is a squarefree strongly stable ideal , ic = i . therefore p and / have the same graded betti numbers , projective dimension and regularity . in this paper , we study the relationship of the betti numbers between ic and i . in section 1 , the concepts of combinatorial shifting and some related results are given
) s为无平方强稳定理想时i ~ c = i ，因而i ~ c和i的分次betti数、投射维数和正则度相同，本文主要研究i为无平方稳定理想时， i ~ c和i之间分次betti数的关系。
In section 3 , we show that when i is a squarefree stable ideal , shiftij ( i ) and i have the same graded betti numbers , projective dimension and regularity , then ic and i have the same graded betti numbers , projective dimension and regularity . at last we apply the results we obtained to simplicial complexes
在第三节中证明了当i为无平方稳定理想时， shiftij ( i )与i的分次betti数、投射维数和正则度相同，从而i ~ c与i的分次betti数、投射维数和正则度相同，最后将所得结论推广到单纯复形上。