In 1954 Lorentz and Erdo s showed that there are very thin sets of positive integers complementary to the set of primes. In particular, there is an A N with (ii) every n n 0 can be written as n=a+ p, a # A, p prime. Erdo s conjectured that the bound (i) could be sharpened to o(ln 2 x) or even O(ln
On the erdos-wintner theorem of probabilistic number theory
✍ Scribed by Harold N. Shapiro
- Publisher
- John Wiley and Sons
- Year
- 1983
- Tongue
- English
- Weight
- 452 KB
- Volume
- 36
- Category
- Article
- ISSN
- 0010-3640
No coin nor oath required. For personal study only.
✦ Synopsis
We would like to take this opportunity to express continuing respect and affection for our colleague, Harold Grad, on the occasion of his sixtieth birthday. Perhaps it is not inappropriate to apologize for the fact that this humble offering comes from the other side (the wrong side?) of the mathematical tracks. In any event, it is comforting to note that the positive integers are still used on his side to count birthdays. It is our sincere hope that in this case a considerably larger segment of the sequence will be required.
📜 SIMILAR VOLUMES
For any integer r \ 1, let a(r) be the largest constant a \ 0 such that if E > 0 and 0 < c < c 0 for some small c 0 =c 0 (r, E) then every graph G of sufficiently large order n and at least edges contains a copy of any (r+1)-chromatic graph H of independence number a(H) [ (a -E) log n log(1/c) .
## Abstract The Erdős‐Rényi and Projective Norm graphs are algebraically defined graphs that have proved useful in supplying constructions in extremal graph theory and Ramsey theory. Their eigenvalues have been computed and this yields an upper bound on their independence number. Here we show that
## Abstract One of the basic results in graph colouring is Brooks' theorem [R. L. Brooks, Proc Cambridge Phil Soc 37 (1941) 194–197], which asserts that the chromatic number of every connected graph, that is not a complete graph or an odd cycle, does not exceed its maximum degree. As an extension o
According to the minimum interaction theory, the chromosome evolution of eukaryotes proceeds as a whole toward increasing the chromosome number. This raises the following two questions: what was the starting chromosome number of eukaryotes and does the chromosome number increase infinitely? We attem