Distinct-Part Partition Calculator

Initialize one empty partition at zero, then update totals in descending order for each candidate positive part. This route excludes repeated parts but still treats reordered sums as the same partition. Inputs remain whole numbers inside the displayed domain, and the page never rounds a decimal into an accepted integer. This keeps the reported result tied to one explicit mathematical definition rather than an unstated convention.

The result is smaller than or equal to the unrestricted partition count because repeated parts such as 5+5 are excluded. List the decompositions for a small target and confirm that no positive part repeats. Reuse the displayed recurrence, congruence, or counting identity with the same inputs. The verification evidence checks this calculator's result, but it does not establish assumptions or conclusions outside the stated mathematical domain.

The target is capped at 100 to keep dynamic-programming work and integer output predictable in the browser. The cap avoids extending a browser table into unsupported large-count work. A finite limit prevents browser stalls and avoids presenting an unsafe floating-point integer as exact. Work beyond that limit belongs in arbitrary-precision software with explicit resource controls and independent validation.