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PartitionsQ

Status: Stable

documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

Description

PartitionsQ[n]
    gives the number q(n) of partitions of the integer n into distinct
parts (equivalently, into odd parts). n must be an integer; q(n) = 0
for n < 0. Threads over lists. For the partitions themselves use
IntegerPartitions[n, All, Range[n]] with distinct parts.

Examples

All examples below are verified against the current Mathilda build.

In[1]:= Table[PartitionsQ[k], {k, 0, 20}]
Out[1]= {1, 1, 1, 2, 2, 3, 4, 5, 6, 8, 10, 12, 15, 18, 22, 27, 32, 38, 46, 54, 64}

In[2]:= PartitionsQ[100]
Out[2]= 444793

In[3]:= PartitionsQ[{2, 4, 6}]
Out[3]= {1, 2, 4}

Implementation notes

  • Protected, Listable — PartitionsQ[{2, 4, 6}] → {1, 2, 4}.
  • Two engines, dispatched by the size of n (threshold n = 1000):
  • Small n — an exact GMP recurrence derived from the Euler identity

Attributes: Listable, Protected.

Implementation status

Stable — documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

References