Partition identities II. The results of Bateman and Erdős
✍ Scribed by Jason P. Bell; Stanley N. Burris
- Publisher
- Elsevier Science
- Year
- 2006
- Tongue
- English
- Weight
- 257 KB
- Volume
- 117
- Category
- Article
- ISSN
- 0022-314X
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
Bateman and Erdo s found necessary and sufficient conditions on a set A for the kth differences of the partitions of n with parts in A, p (k) A (n), to eventually be positive; moreover, they showed that when these conditions occur p (k+1) A (n) tends to zero as n tends to infinity. Bateman and Erdo
We employ the probabilistic method to prove a stronger version of a result of Helm, related to a conjecture of Erdos and Turan about additive bases of the positive integers. We show that for a class of random sequences of positive integers \(A\), which satisfy \(|A \cap[1, x]| \gg \sqrt{x}\) with pr