Partition¶

prtition.spad line 1 [edit on github]

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: from CoercibleTo OutputForm

conjugate: % -> %: conjugate(p) returns the conjugate partition of a partition p

convert: % -> List Integer: from ConvertibleTo List Integer

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.