1
vote
1answer
161 views

Does the asymptotic formula for Partitions into parts <c exist?

A partition of $n$ is a weakly decreasing tuple of numbers $(\lambda_1,\lambda_2,\lambda_3,....\lambda_k)$ whose sum is $n.$ A natural problem studied is counting partitions whose summands ...
1
vote
1answer
142 views

Distribution of colors in the number of integer partitions of n

Given an integer $n$ the number of partitions of $n$ into two colors can be represented as $$p_2(n)=\sum_{k=0}^n p(k)p(n-k)$$ where $p(k)$ counts the number of ordinary partitions of $k.$ What is the ...
4
votes
2answers
546 views

How local the property of “being a partition” is?

Note: The problem is solved! See EDIT below. The following question about integer partitions arose from a purely "practical" question: Does there exist better dynamic programming algorithms for the ...
7
votes
3answers
727 views

Binomial coefficient in Andrews' partition book

First of all, i think MathOverflow is a very great community to discuss math, either basic or advanced, and i'm glad to participate here. It's my first post, so i'm sorry if i did anything wrong, and ...