MatrixSchubert : Table of Contents

• MatrixSchubert -- matrix Schubert varieties and ASM varieties
• antiDiagInit -- compute the (unique) antidiagonal initial ideal of an ASM ideal
• ASMFullList -- lists all ASMs of a fixed size
• ASMRandomList -- lists random ASMs of a fixed size
• ASMToMonotoneTriangle -- converts an ASM to a monotone triangle
• augmentedEssentialSet -- find the essential set of a partial alternating sign matrix or a permutation together with the rank conditions determining the alternating sign matrix variety
• augmentedRotheDiagram -- find the Rothe diagram of a partial alternating sign matrix together with the rank table determining the alternating sign matrix variety
• avoidsAllPatterns -- whether a permutation avoids all of the given patterns
• cohenMacaulayASMsList -- lists all Cohen-Macaulay ASMs of a fixed size which are not permutation matrices
• composePerms -- computes the composition of two permutations
• descentSet -- the descent set of a permutation
• diagLexInitNW -- Diagonal initial ideal of an ASM ideal with respect to lex, starting from NW corner
• diagLexInitSE -- Diagonal initial ideal of an ASM ideal with respect to lex, starting from SE corner
• diagRevLexInit -- Diagonal initial ideal of an ASM ideal with respect to revlex, ordering variables from NW corner
• doubleSchubertPolynomial -- computes the double Schubert polynomial of a permutation
• entrywiseMaxRankTable -- compute the entrywise maximum rank table of a list of ASMs
• entrywiseMinRankTable -- compute the entrywise minimum rank table of a list of ASMs
• essentialSet -- compute the essential set in the Rothe Diagram for a partial alternating sign matrix or a permutation.
• firstDescent -- finds the location of the first descent of a permutation
• fultonGens -- compute the Fulton generators of an ASM ideal (for example, a Schubert determinantal ideal)
• Functions for investigating permutations -- basic functions for permutations
• getASM -- get the ASM of an ideal (if it exists)
• grothendieckPolynomial -- computes the Grothendieck polynomial of a permutation
• Initial ideals of ASM ideals -- basic functions for investigating initial ideals of ASM varieties
• initialIdealsList -- lists all antidiagonal initial ideals of ASMs of a fixed size
• inverseOf -- to return the inverse of a permutation in 1-line notation.
• Investigating ASM varieties -- basic functions for alternating sign matrix ideals
• Investigating matrix Schubert varieties -- basic functions for Schubert determinantal ideals
• isASM -- whether a matrix is an ASM
• isASMIdeal -- whether an ideal is an ASM ideal
• isASMUnion -- whether the union of matrix Schubert varieties is an ASM variety
• isCartwrightSturmfels -- whether a permutation is Cartwright-Sturmfels
• isCDG -- whether a permutation is CDG
• isIntersectionOfSchubertDeterminantalIdeals -- whether an ideal is the intersection of Schubert determinantal ideals
• isMinRankTable -- whether a matrix is the canonical rank table of some partial ASM
• isPartialASM -- whether a matrix is a partial alternating sign matrix
• isPatternAvoiding -- whether a permutation avoids certain patterns, e.g. $2143$-avoiding or $312$- and $231$-avoiding
• isPerm -- whether a list is a permutation in 1-line notation
• isSchubertCM -- whether an ASM variety is Cohen-Macaulay
• isVexillary -- whether a permutation is vexillary, i.e. 2143-avoiding
• KPolynomialASM -- compute the K Polynomial of an ASM variety
• lastDescent -- finds the location of the last descent of a permutation
• longestPerm -- to return the longest permutation of length n
• monotoneTriangleToASM -- converts a monotone triangle to an ASM
• nonCohenMacaulayASMsList -- lists all non-Cohen-Macaulay ASMs of a fixed size
• padASM -- pad an ASM with an identity matrix
• partialASMToASM -- extend a partial alternating sign matrix to an alternating sign matrix
• permLength -- to find the length of a permutation in 1-line notation.
• permSetOfASM -- finds the permutation set of an alternating sign matrix
• permToMatrix -- converts a permutation in 1-line notation into a permutation matrix
• PipeDream -- the class representing a pipe dream

  • pipeDreams -- computes the set of reduced pipe dreams corresponding to a permutation
  • pipeDreamsNonReduced -- computes the set of all pipe dreams corresponding to a permutation
• rajcode -- finds the Rajchgot code of a permutation
• rajIndex -- finds the Rajchgot index of a permutation
• rankTable -- compute a table of rank conditions that determines a Schubert determinantal ideal or, more generally, an alternating sign matrix ideal.
• rankTableFromMatrix -- returns the minimal rank table from an arbitrary integer matrix
• rankTableToASM -- to find the a partial ASM associated to a given rank table
• rotheDiagram -- find the Rothe diagram of a partial alternating sign matrix
• schubertAdd -- compute the sum of ASM ideals
• schubertCodim -- compute the codimension (i.e., height) of a Schubert determinantal ideal or ASM ideal
• schubertDecompose -- finds the decomposition of an ASM ideal into Schubert determinantal ideals
• schubertDeterminantalIdeal -- compute an alternating sign matrix ideal (for example, a Schubert determinantal ideal)
• schubertIntersect -- compute the intersection of ASM ideals
• schubertPolynomial -- computes the Schubert polynomial of a permutation
• schubertRegularity -- compute the Castelnuovo-Mumford regularity of the quotient by a Schubert determinantal ideal or ASM ideal
• subwordComplex -- to find the subword complex associated to w
• toOneLineNotation -- rewrites a transposition in 1-line notation
• toOneLineNotation(Matrix) -- converts a permutation to one line notation