Curvature, Diameter and Bounded Betti Numbers
β Scribed by Zhongmin Shen; Jyh-Yang Wu*
- Publisher
- Coastal and Estuarine Research Federation
- Year
- 2006
- Tongue
- English
- Weight
- 221 KB
- Volume
- 27
- Category
- Article
- ISSN
- 1860-6261
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
In this paper we prove parts of a conjecture of Herzog giving lower bounds on the rank of the free modules appearing in the linear strand of a graded kth syzygy module over the polynomial ring. If in addition the module is β«ήβ¬ n -graded we show that the conjecture holds in full generality. Furthermo
We show that any algebraic computation tree or any fixed-degree algebraic tree for solving the membership question of a compact set S R n must have height greater than 0(log(; i (S)))&cn for each i, where ; i (S) is the ith Betti number. This generalizes a well-known result by Ben-Or who proved this