Combinatorial complexity in o-minimal geometry
组合数学
2014-02-26 v2 逻辑
摘要
In this paper we prove tight bounds on the combinatorial and topological complexity of sets defined in terms of definable sets belonging to some fixed definable family of sets in an o-minimal structure. This generalizes the combinatorial parts of similar bounds known in the case of semi-algebraic and semi-Pfaffian sets, and as a result vastly increases the applicability of results on combinatorial and topological complexity of arrangements studied in discrete and computational geometry. As a sample application, we extend a Ramsey-type theorem due to Alon et al., originally proved for semi-algebraic sets of fixed description complexity to this more general setting.
引用
@article{arxiv.math/0612050,
title = {Combinatorial complexity in o-minimal geometry},
author = {Saugata Basu},
journal= {arXiv preprint arXiv:math/0612050},
year = {2014}
}
备注
25 pages. Revised version. To appear in the Proc. London Math. Soc