# Partition¶

Partition is an OrderedCancellationAbelianMonoid which is used as the basis for symmetric polynomial representation of the sums of powers in SymmetricPolynomial. Thus, (5 2 2 1) will represent s5 * s2^2 * s1.

0: %

from AbelianMonoid

*: (NonNegativeInteger, %) -> %

from AbelianMonoid

*: (PositiveInteger, %) -> %

from AbelianSemiGroup

+: (%, %) -> %

from AbelianSemiGroup

<=: (%, %) -> Boolean

from PartialOrder

<: (%, %) -> Boolean

from PartialOrder

=: (%, %) -> Boolean

from BasicType

>=: (%, %) -> Boolean

from PartialOrder

>: (%, %) -> Boolean

from PartialOrder

~=: (%, %) -> Boolean

from BasicType

coerce: % -> List Integer

coerce(p) coerces a partition into a list of integers

coerce: % -> OutputForm
conjugate: % -> %

conjugate(p) returns the conjugate partition of a partition p

convert: % -> List Integer
hash: % -> SingleInteger

from SetCategory

hashUpdate!: (HashState, %) -> HashState

from SetCategory

latex: % -> String

from SetCategory

max: (%, %) -> %

from OrderedSet

min: (%, %) -> %

from OrderedSet

opposite?: (%, %) -> Boolean

from AbelianMonoid

partition: List Integer -> %

partition(li) converts a list of integers li to a partition

pdct: % -> Integer

pdct(a1^n1 a2^n2 ...) returns n1! * a1^n1 * n2! * a2^n2 * .... This function is used in the package CycleIndicators.

powers: List Integer -> List List Integer

powers(li) returns a list of 2-element lists. For each 2-element list, the first element is an entry of li and the second element is the multiplicity with which the first element occurs in li. There is a 2-element list for each value occurring in l.

sample: %

from AbelianMonoid

smaller?: (%, %) -> Boolean

from Comparable

subtractIfCan: (%, %) -> Union(%, failed)
zero?: % -> Boolean

from AbelianMonoid

AbelianMonoid

AbelianSemiGroup

BasicType

CancellationAbelianMonoid

Comparable

OrderedAbelianMonoid

OrderedAbelianSemiGroup

OrderedCancellationAbelianMonoid

OrderedSet

PartialOrder

SetCategory