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Permutations : Table of Contents
Permutations
-- a package which implements permutations
ascendingRuns
-- computes the ascending runs of a permutation
ascents
-- computes the ascents of a permutation
Ascents, descents, runs, exceedances, and records
-- a detailed overview of permutations in Macaulay2
avoidsPattern
-- whether a permutation avoids a pattern
avoidsPatterns
-- whether a permutation simultaneously avoids a list of patterns
Basic operations
-- an overview of basic operations with permutations
Bruhat order
-- an overview of the Bruhat order for permutations
Creating permutations
-- an overview of creating permutations
cycleDecomposition
-- computes the decomposition of a permutation as a product of disjoint cycles
cycleType
-- computes the cycle type of a permutation
Cyclic decomposition
-- an overview of cyclic decompositions of permutations
descendingRuns
-- computes the descending runs of a permutation
descents
-- computes the descents of a permutation
exceedances
-- computes the exceedances of a permutation
extend
-- rewrites a permutation as a permutation on more symbols
extend(Permutation,Permutation)
-- rewrites two permutations to be permutations on the same number of symbols
fixedPoints
-- computes the fixed points of a permutation
foataBijection
-- computes the image of a permutation under the Foata bijection
Group actions
-- an overview of permutations acting on objects in Macaulay2
inverse(Permutation)
-- computes the inverse of a permutation
inversions
-- computes the inversions of a permutation
isCartwrightSturmfels
-- whether a permutation is Cartwright-Sturmfels
isCDG
-- whether a permutation is CDG.
isDerangement
-- whether a permutation is a derangement
isEven
-- whether a permutation is even
isOdd
-- whether a permutation is odd
isSeparable
-- whether a permutation is separable.
isVexillary
-- whether a permutation is vexillary
isWellDefined(Permutation)
-- checks if a list is a valid permutation
length(Permutation)
-- computes the length of a permutation
Matrix * Permutation
-- computes the action of a permutation on the columns of a matrix
Matrix ^ Permutation
-- computes the action of a permutation on a matrix
Matrix _ Permutation
-- computes the action of a permutation on the rows of a matrix
matrix(Permutation)
-- computes the matrix representation of a permutation
Miscellaneous
-- a detailed overview of permutations in Macaulay2
ord
-- computes the order of a permutation
Pattern avoidance
-- an overview of pattern avoidance for permutations in Macaulay2
Permutation
-- the Permutation type
Permutation * Matrix
-- computes the action of a permutation on the rows of a matrix
Permutation * Permutation
-- computes the product of two permutations
Permutation * VisibleList
-- computes the action of a permutation on a list
Permutation == Permutation
-- whether two permutations are the same
Permutation ^ ZZ
-- computes the power of a permutation
Permutation _ List
-- selects a subset of the permutation when regarded as a list
Permutation _ Sequence
-- selects a subset of the permutation when regarded as a list
Permutation _ ZZ
-- selects an element from the permutation when regarded as a list
Permutations Guide
-- a detailed overview of permutations in Macaulay2
randomPermutation
-- generates a random permutation
records
-- computes the saliances of a permutation
reducedWords
-- computes the reduced words of a permutation
saliances
-- computes the saliances of a permutation
sign(Permutation)
-- computes the sign of a permutation
strongBruhatOrder
-- compares two permutations in the (strong) Bruhat order
symmetricGroupPoset
-- constructs the poset of the symmetric group under a partial order
transposition
-- constructs a transposition
trim
-- rewrites a permutation in its smallest representation
VisibleList _ Permutation
-- computes the action of a permutation on a list
Weak
(missing documentation)
weakBruhatOrder
-- compares two permutations in the weak Bruhat order