The number of orthogonal permutations
β Scribed by Akihiro Nozaki; Masahiro Miyakawa; Grant Pogosyan; Ivo G Rosenberg
- Publisher
- Elsevier Science
- Year
- 1995
- Tongue
- English
- Weight
- 652 KB
- Volume
- 16
- Category
- Article
- ISSN
- 0195-6698
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Let \_ # S k and { # S n be permutations. We say { contains \_ if there exist Stanley and Wilf conjectured that for any \_ # S k there exists a constant c=c(\_) such that F(n, \_) c n for all n. Here we prove the following weaker statement: For every fixed \_ # S k , F(n, \_) c n#\* (n) , where c=c
We prove that a suitably separated family of n compact convex sets in R d can be met by k-flat transversals in at most d&k) , or for fixed k and d, O(n k(k+1)(d&k) ) different order types. This is the first non-trivial upper bound for 12.