The number of polytopes, configurations and real matroids
作者:
Noga Alon,
期刊:
Mathematika
(WILEY Available online 1986)
卷期:
Volume 33,
issue 1
页码: 62-71
ISSN:0025-5793
年代: 1986
DOI:10.1112/S0025579300013875
出版商: London Mathematical Society
数据来源: WILEY
摘要:
AbstractWe show that the number of combinatorially distinct labelledd‐polytopes onnvertices is at most(n/d)d2n(1+o(1)), asn/d→ ∞. A similar bound for the number of simplicial polytopes has previously been proved by Goodman and Pollack. This bound improves considerably the previous known bounds. We also obtain sharp upper and lower bounds for the numbers of real oriented and unoriented matroids withnelements of rankd. Our main tool is a theorem of Milnor and Thorn from real algebraic geometry.
点击下载:
PDF
(560KB)
返 回