Como usar (3 passos)
- Choose Partition or Composition, then select the constraint you need.
- Enter n (and k/m/a/b when required), then pick count, table, enumeration, or sample.
- Exporte CSV/TSV ou copie uma URL compartilhável para a aula ou suas anotações.
Entradas
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Table
Exemplos
Key formulas and notes
- Partition counts use dynamic programming: p(n, m) = p(n, m-1) + p(n-m, m).
- Compositions count is 2^(n-1) for n >= 1, and k parts use C(n-1, k-1).
- Distinct parts and odd parts have the same count (Euler's identity).
- Enumeration is limited for speed; use samples for larger n.
Perguntas frequentes
O que é the difference between partitions and compositions?
Partitions ignore order (3+1 equals 1+3), while compositions treat different orders as distinct.
What does p(n) mean?
p(n) is the number of integer partitions of n, also called the partition number.
How Devo count partitions into exactly k parts?
Select p(n, k) and enter k to count partitions with exactly k parts.
How do distinct partitions work?
Distinct partitions require every part size to be unique. The count equals the odd-part count.
O que é a Ferrers (Young) diagram?
It draws each part as a row of dots or squares, making the partition shape visible.
Why is composition count 2^(n-1)?
There are n-1 gaps between ones, and each gap either has a divider or not.
Why is enumeration limited for large n?
The number of partitions grows quickly, so enumeration is capped to keep the page fast.
Posso Calcular values modulo m?
Yes. Switch to modulo mode and enter m to Calcular Resultados mod m.