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Asymptotic results for partitions (II) and a conjecture of Bateman and Erdös

✍ Scribed by L.B Richmond


Publisher
Elsevier Science
Year
1976
Tongue
English
Weight
249 KB
Volume
8
Category
Article
ISSN
0022-314X

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📜 SIMILAR VOLUMES


A Proof of a Partition Conjecture of Bat
✍ Jason P Bell 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 97 KB

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

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We show that every graph G of size at least 256 p 2 |G| contains a topological complete subgraph of order p. This slight improvement of a recent result of Komlós and Szemerédi proves a conjecture made by Mader and by Erdös and Hajnal.