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MatrixSchubert : Index

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Algorithm -- computes the Grothendieck polynomial of a permutation
antiDiagInit -- compute the (unique) antidiagonal initial ideal of an ASM ideal
antiDiagInit(...,CoefficientRing=>...) -- compute the (unique) antidiagonal initial ideal of an ASM ideal
antiDiagInit(...,Variable=>...) -- compute the (unique) antidiagonal initial ideal of an ASM ideal
antiDiagInit(List) -- compute the (unique) antidiagonal initial ideal of an ASM ideal
antiDiagInit(Matrix) -- compute the (unique) antidiagonal initial ideal of an ASM ideal
ASMFullList -- lists all ASMs of a fixed size
ASMFullList(ZZ) -- lists all ASMs of a fixed size
ASMRandomList -- lists random ASMs of a fixed size
ASMRandomList(ZZ,ZZ) -- lists random ASMs of a fixed size
ASMToMonotoneTriangle -- converts an ASM to a monotone triangle
ASMToMonotoneTriangle(Matrix) -- 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
augmentedEssentialSet(List) -- find the essential set of a partial alternating sign matrix or a permutation together with the rank conditions determining the alternating sign matrix variety
augmentedEssentialSet(Matrix) -- 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
augmentedRotheDiagram(List) -- find the Rothe diagram of a partial alternating sign matrix together with the rank table determining the alternating sign matrix variety
augmentedRotheDiagram(Matrix) -- 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
avoidsAllPatterns(List,List) -- whether a permutation avoids all of the given patterns
CoefficientRing -- Diagonal initial ideal of an ASM ideal with respect to revlex, ordering variables from NW corner
cohenMacaulayASMsList -- lists all Cohen-Macaulay ASMs of a fixed size which are not permutation matrices
cohenMacaulayASMsList(ZZ) -- lists all Cohen-Macaulay ASMs of a fixed size which are not permutation matrices
composePerms -- computes the composition of two permutations
composePerms(List,List) -- computes the composition of two permutations
descentSet -- the descent set of a permutation
descentSet(List) -- the descent set of a permutation
diagLexInitNW -- Diagonal initial ideal of an ASM ideal with respect to lex, starting from NW corner
diagLexInitNW(...,CoefficientRing=>...) -- Diagonal initial ideal of an ASM ideal with respect to lex, starting from NW corner
diagLexInitNW(...,Variable=>...) -- Diagonal initial ideal of an ASM ideal with respect to lex, starting from NW corner
diagLexInitNW(List) -- Diagonal initial ideal of an ASM ideal with respect to lex, starting from NW corner
diagLexInitNW(Matrix) -- 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
diagLexInitSE(...,CoefficientRing=>...) -- Diagonal initial ideal of an ASM ideal with respect to lex, starting from SE corner
diagLexInitSE(...,Variable=>...) -- Diagonal initial ideal of an ASM ideal with respect to lex, starting from SE corner
diagLexInitSE(List) -- Diagonal initial ideal of an ASM ideal with respect to lex, starting from SE corner
diagLexInitSE(Matrix) -- 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
diagRevLexInit(...,CoefficientRing=>...) -- Diagonal initial ideal of an ASM ideal with respect to revlex, ordering variables from NW corner
diagRevLexInit(...,Variable=>...) -- Diagonal initial ideal of an ASM ideal with respect to revlex, ordering variables from NW corner
diagRevLexInit(List) -- Diagonal initial ideal of an ASM ideal with respect to revlex, ordering variables from NW corner
diagRevLexInit(Matrix) -- 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
doubleSchubertPolynomial(List) -- computes the double Schubert polynomial of a permutation
entrywiseMaxRankTable -- compute the entrywise maximum rank table of a list of ASMs
entrywiseMaxRankTable(List) -- compute the entrywise maximum rank table of a list of ASMs
entrywiseMinRankTable -- compute the entrywise minimum rank table of a list of ASMs
entrywiseMinRankTable(List) -- 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.
essentialSet(List) -- compute the essential set in the Rothe Diagram for a partial alternating sign matrix or a permutation.
essentialSet(Matrix) -- 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
firstDescent(List) -- 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)
fultonGens(...,CoefficientRing=>...) -- compute the Fulton generators of an ASM ideal (for example, a Schubert determinantal ideal)
fultonGens(...,Variable=>...) -- compute the Fulton generators of an ASM ideal (for example, a Schubert determinantal ideal)
fultonGens(List) -- compute the Fulton generators of an ASM ideal (for example, a Schubert determinantal ideal)
fultonGens(Matrix) -- 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)
getASM(Ideal) -- get the ASM of an ideal (if it exists)
grothendieckPolynomial -- computes the Grothendieck polynomial of a permutation
grothendieckPolynomial(...,Algorithm=>...) -- computes the Grothendieck polynomial of a permutation
grothendieckPolynomial(List) -- 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
initialIdealsList(ZZ) -- lists all antidiagonal initial ideals of ASMs of a fixed size
inverseOf -- to return the inverse of a permutation in 1-line notation.
inverseOf(List) -- 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
isASM(Matrix) -- whether a matrix is an ASM
isASMIdeal -- whether an ideal is an ASM ideal
isASMIdeal(Ideal) -- whether an ideal is an ASM ideal
isASMUnion -- whether the union of matrix Schubert varieties is an ASM variety
isASMUnion(List) -- whether the union of matrix Schubert varieties is an ASM variety
isCartwrightSturmfels -- whether a permutation is Cartwright-Sturmfels
isCartwrightSturmfels(List) -- whether a permutation is Cartwright-Sturmfels
isCDG -- whether a permutation is CDG
isCDG(List) -- whether a permutation is CDG
isIntersectionOfSchubertDeterminantalIdeals -- whether an ideal is the intersection of Schubert determinantal ideals
isIntersectionOfSchubertDeterminantalIdeals(Ideal) -- whether an ideal is the intersection of Schubert determinantal ideals
isMinRankTable -- whether a matrix is the canonical rank table of some partial ASM
isMinRankTable(Matrix) -- whether a matrix is the canonical rank table of some partial ASM
isPartialASM -- whether a matrix is a partial alternating sign matrix
isPartialASM(Matrix) -- 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
isPatternAvoiding(List,List) -- 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
isPerm(List) -- whether a list is a permutation in 1-line notation
isSchubertCM -- whether an ASM variety is Cohen-Macaulay
isSchubertCM(List) -- whether an ASM variety is Cohen-Macaulay
isSchubertCM(Matrix) -- whether an ASM variety is Cohen-Macaulay
isVexillary -- whether a permutation is vexillary, i.e. 2143-avoiding
isVexillary(List) -- whether a permutation is vexillary, i.e. 2143-avoiding
KPolynomialASM -- compute the K Polynomial of an ASM variety
KPolynomialASM(Matrix) -- compute the K Polynomial of an ASM variety
lastDescent -- finds the location of the last descent of a permutation
lastDescent(List) -- finds the location of the last descent of a permutation
longestPerm -- to return the longest permutation of length n
longestPerm(ZZ) -- to return the longest permutation of length n
MatrixSchubert -- matrix Schubert varieties and ASM varieties
monotoneTriangleToASM -- converts a monotone triangle to an ASM
monotoneTriangleToASM(List) -- converts a monotone triangle to an ASM
nonCohenMacaulayASMsList -- lists all non-Cohen-Macaulay ASMs of a fixed size
nonCohenMacaulayASMsList(ZZ) -- lists all non-Cohen-Macaulay ASMs of a fixed size
padASM -- pad an ASM with an identity matrix
padASM(Matrix,ZZ) -- pad an ASM with an identity matrix
partialASMToASM -- extend a partial alternating sign matrix to an alternating sign matrix
partialASMToASM(Matrix) -- extend a partial alternating sign matrix to an alternating sign matrix
permLength -- to find the length of a permutation in 1-line notation.
permLength(List) -- to find the length of a permutation in 1-line notation.
permSetOfASM -- finds the permutation set of an alternating sign matrix
permSetOfASM(Matrix) -- finds the permutation set of an alternating sign matrix
permToMatrix -- converts a permutation in 1-line notation into a permutation matrix
permToMatrix(List) -- 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
pipeDreams(List) -- computes the set of reduced pipe dreams corresponding to a permutation
pipeDreamsNonReduced -- computes the set of all pipe dreams corresponding to a permutation
pipeDreamsNonReduced(List) -- computes the set of all pipe dreams corresponding to a permutation
rajcode -- finds the Rajchgot code of a permutation
rajcode(List) -- finds the Rajchgot code of a permutation
rajIndex -- finds the Rajchgot index of a permutation
rajIndex(List) -- 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.
rankTable(List) -- compute a table of rank conditions that determines a Schubert determinantal ideal or, more generally, an alternating sign matrix ideal.
rankTable(Matrix) -- 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
rankTableFromMatrix(Matrix) -- returns the minimal rank table from an arbitrary integer matrix
rankTableToASM -- to find the a partial ASM associated to a given rank table
rankTableToASM(Matrix) -- to find the a partial ASM associated to a given rank table
rotheDiagram -- find the Rothe diagram of a partial alternating sign matrix
rotheDiagram(List) -- find the Rothe diagram of a partial alternating sign matrix
rotheDiagram(Matrix) -- find the Rothe diagram of a partial alternating sign matrix
schubertAdd -- compute the sum of ASM ideals
schubertAdd(List) -- compute the sum of ASM ideals
schubertCodim -- compute the codimension (i.e., height) of a Schubert determinantal ideal or ASM ideal
schubertCodim(List) -- compute the codimension (i.e., height) of a Schubert determinantal ideal or ASM ideal
schubertCodim(Matrix) -- 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
schubertDecompose(Ideal) -- finds the decomposition of an ASM ideal into Schubert determinantal ideals
schubertDecompose(Matrix) -- finds the decomposition of an ASM ideal into Schubert determinantal ideals
schubertDeterminantalIdeal -- compute an alternating sign matrix ideal (for example, a Schubert determinantal ideal)
schubertDeterminantalIdeal(...,CoefficientRing=>...) -- compute an alternating sign matrix ideal (for example, a Schubert determinantal ideal)
schubertDeterminantalIdeal(...,Variable=>...) -- compute an alternating sign matrix ideal (for example, a Schubert determinantal ideal)
schubertDeterminantalIdeal(List) -- compute an alternating sign matrix ideal (for example, a Schubert determinantal ideal)
schubertDeterminantalIdeal(Matrix) -- compute an alternating sign matrix ideal (for example, a Schubert determinantal ideal)
schubertIntersect -- compute the intersection of ASM ideals
schubertIntersect(List) -- compute the intersection of ASM ideals
schubertPolynomial -- computes the Schubert polynomial of a permutation
schubertPolynomial(...,Algorithm=>...) -- computes the Schubert polynomial of a permutation
schubertPolynomial(List) -- computes the Schubert polynomial of a permutation
schubertRegularity -- compute the Castelnuovo-Mumford regularity of the quotient by a Schubert determinantal ideal or ASM ideal
schubertRegularity(List) -- compute the Castelnuovo-Mumford regularity of the quotient by a Schubert determinantal ideal or ASM ideal
schubertRegularity(Matrix) -- 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
subwordComplex(List) -- to find the subword complex associated to w
toOneLineNotation -- rewrites a transposition in 1-line notation
toOneLineNotation(List,ZZ) -- rewrites a transposition in 1-line notation
toOneLineNotation(Matrix) -- converts a permutation to one line notation
Variable -- Diagonal initial ideal of an ASM ideal with respect to revlex, ordering variables from NW corner