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Mathematica > Mathematics and Algorithms > Number Theory >

Built-in Mathematica Symbol

PartitionsQ

PartitionsQ[n]
gives the number q(n) of partitions of the integer n into distinct parts.

Integer mathematical function, suitable for both symbolic and numerical manipulation.

Plot the number of restricted partitions:

Plot the number of restricted partitions:

Compute the number of partitions for large numbers:

PartitionsQ threads element-wise over lists:

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:

PartitionsQ gives the length of IntegerPartitions with nonrepeating parts:

Generate the explicit partitions:

Model PartitionsQ based on the definition:

PartitionsQ evaluates only for explicit integers:

Use Simplify to find implicit integers in arguments:

Successive differences of PartitionsQ modulo 2:

A "random" walk based on PartitionsQ: