PartitionsQ [n]
gives the number q(n) of partitions of the integer n into distinct parts.
PartitionsQ
PartitionsQ [n]
gives the number q(n) of partitions of the integer n into distinct parts.
Details
- Integer mathematical function, suitable for both symbolic and numerical manipulation.
- PartitionsQ automatically threads over lists.
Examples
open all close allBasic Examples (2)
Plot the number of restricted partitions:
Scope (3)
Compute the number of partitions for large numbers:
PartitionsQ threads element-wise over lists:
TraditionalForm formatting:
Applications (3)
Compare cumulative counts of even and odd partitions into distinct parts:
Plot the ratio of the number of partitions with its asymptotic value:
Visualize p-adic valuations of the number of partitions:
Properties & Relations (4)
PartitionsQ gives the length of IntegerPartitions with nonrepeating parts:
Generate the explicit partitions:
Model PartitionsQ based on the definition:
Obtain values of PartitionsQ from series expansion:
FindSequenceFunction can recognize the PartitionsQ sequence:
Possible Issues (1)
PartitionsQ evaluates only for explicit integers:
Use Simplify to find implicit integers in arguments:
Neat Examples (2)
Successive differences of PartitionsQ modulo 2:
A "random" walk based on PartitionsQ :
See Also
Tech Notes
Related Guides
Related Links
History
Introduced in 1988 (1.0)
Text
Wolfram Research (1988), PartitionsQ, Wolfram Language function, https://reference.wolfram.com/language/ref/PartitionsQ.html.
CMS
Wolfram Language. 1988. "PartitionsQ." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/PartitionsQ.html.
APA
Wolfram Language. (1988). PartitionsQ. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/PartitionsQ.html
BibTeX
@misc{reference.wolfram_2025_partitionsq, author="Wolfram Research", title="{PartitionsQ}", year="1988", howpublished="\url{https://reference.wolfram.com/language/ref/PartitionsQ.html}", note=[Accessed: 16-November-2025]}
BibLaTeX
@online{reference.wolfram_2025_partitionsq, organization={Wolfram Research}, title={PartitionsQ}, year={1988}, url={https://reference.wolfram.com/language/ref/PartitionsQ.html}, note=[Accessed: 16-November-2025]}