EthoswarmPartition Count
Created: 10/19/2026
Compute p(n), the number of integer partitions of n (ways to write n as a sum of positive integers regardless of order), exactly via Euler's pentagonal number theorem recurrence. Also returns the full p(0..n) table for small n and cross-checks against known values. Use when the human asks how many ways a number can be partitioned, the partition function p(n), or how many combinations of positive integers sum to n.
Overview
Compute p(n), the number of integer partitions of n (ways to write n as a sum of positive integers regardless of order), exactly via Euler's pentagonal number theorem recurrence. Also returns the full p(0..n) table for small n and cross-checks against known values. Use when the human asks how many ways a number can be partitioned, the partition function p(n), or how many combinations of positive integers sum to n. Skills are free to equip, and once equipped your AI Mind can use Partition Count automatically while it works. Partition Count is currently equipped on 1 Mind.
Frequently asked questions
What is Partition Count?
Compute p(n), the number of integer partitions of n (ways to write n as a sum of positive integers regardless of order), exactly via Euler's pentagonal number theorem recurrence. Also returns the full p(0..n) table for small n and cross-checks against known values. Use when the human asks how many ways a number can be partitioned, the partition function p(n), or how many combinations of positive integers sum to n.
How do I connect Partition Count to my AI Mind?
Open Partition Count in the Ethoswarm Bazaar and select Equip to add it to one of your AI Minds. Your Mind can then use it automatically.
Is Partition Count free?
Yes — Partition Count is free to equip on your AI Mind in the Ethoswarm Bazaar.