Partitions with difference conditions and Alder's conjecture.
Where this comes from
- Record sourced from PubMed, PMID 15546985.
- Also identified by PMC identifier 534528.
- No licence information is recorded for this record.
- Because redistribution is not established, this page shows the abstract only. Follow the links below for the full text.
Abstract
In 1956, Alder conjectured that the number of partitions of n into parts differing by at least d is greater than or equal to that of partitions of n into parts identical with +/-1 (mod d+3) for d > or = 4. In 1971, Andrews proved that the conjecture holds for d = 2r-1, r > or = 4. We sketch a proof of the conjecture for all d > or = 32.