We show that the maximum size of a B 2 -sequence of binary n-vectors for large enough n is at most 2 0.5753n , thus improving on the previous bound 2 0.6n due to B. Lindstro m.
An Upper Bound for B2[2] Sequences
β Scribed by Javier Cilleruelo
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 89 KB
- Volume
- 89
- Category
- Article
- ISSN
- 0097-3165
No coin nor oath required. For personal study only.
β¦ Synopsis
We introduce a new counting method to deal with B 2 [2] sequences, getting a new upper bound for the size of these sequences, F(N, 2) -6N+1.
π SIMILAR VOLUMES
Let F h (N) be the maximum number of elements that can be selected from the set [1, ..., N] such that all the sums a 1 + } } } +a h , a 1 } } } a h are different. We introduce new combinatorial and analytic ideas to prove new upper bounds for F h (N). In particular we prove Besides, our techniques
We give a non-trivial upper bound for F h Γ°g; NΓ, the size of a B h Β½g subset of f1; . . . ; Ng, when g > 1. In particular, we prove F 2 Γ°g; NΓ41:864Γ°gNΓ 1=2 ΓΎ 1, and F h Γ°g; NΓ4 1 Γ°1ΓΎcos h Γ°p=hΓΓ 1=h Γ°hh!gNΓ 1=h , h > 2. On the other hand, we exhibit B 2 Β½g subsets of f1; . . .
New upper bounds for the ramsey numbers r ( k , I ) are obtained. In particular it is shown there is a constant A such that The ramsey number r(k, l ) is the smallest integer n, such that any coloring with red and blue of the edges of the complete graph K , of order n yields either a red K , subgra
The upper bound inequality h i (P)&h i&1 (P) ( n&d+i&2 i ) (0 i dΓ2) is proved for the toric h-vector of a rational convex d-dimensional polytope with n vertices. This gives nonlinear inequalities on flag vectors of rational polytopes. ## 1998 Academic Press A major result in polytope theory is th