This entry is about the notion in number theory/combinatorics. For partition functions in the sense of statistical mechanics and quantum field theory see at partition function.
Basic structures
Generating functions
Proof techniques
Combinatorial identities
Polytopes
transfinite arithmetic, cardinal arithmetic, ordinal arithmetic
prime field, p-adic integer, p-adic rational number, p-adic complex number
arithmetic geometry, function field analogy
In number theory/combinatorics, the function which assigns to a natural number the number of its partitions (into multisets of positive natural numbers) is often called the paritition function.
Its (ordinary) generating function is
An asymptotic expansion of the partition function is (Hardy & Ramanujan 1918, see DeSalvo 20 for discussion)
See also:
Asymptotic behaviour:
Godfrey Hardy, Srinivasa Ramanujan, Asymptotic formulaæ in combinatory analysis, Proceedings of the London Mathematical Society, 2(1):75–115, 1918 (doi:10.1112/plms/s2-17.1.75, pdf)
Stephen DeSalvo, Will the real Hardy-Ramanujan formula please stand up? (arXiv:2003.06908)
Created on June 3, 2021 at 10:44:05. See the history of this page for a list of all contributions to it.