Posets : Table of Contents

• Posets -- a package for working with partially ordered sets
• adjoinMax -- computes the poset with a new maximum element
• adjoinMin -- computes the poset with a new minimum element
• allRelations -- computes all relations of a poset
• antichains -- computes all antichains of a poset
• areIsomorphic -- determines if two posets are isomorphic
• atoms -- computes the list of elements covering the minimal elements of a poset
• augmentPoset -- computes the poset with an adjoined minimum and maximum
• booleanLattice -- generates the boolean lattice on $n$ elements
• boundedRegions -- computes the number of bounded regions a hyperplane arrangement divides the space into
• chain -- generates the chain poset on $n$ elements
• chains -- computes all chains of a poset
• characteristicPolynomial -- computes the characteristic polynomial of a ranked poset with a unique minimal element
• closedInterval -- computes the subposet contained between two points
• comparabilityGraph -- produces the comparability graph of a poset
• compare -- compares two elements in a poset
• connectedComponents(Poset) -- generates a list of connected components of a poset
• coveringRelations -- computes the minimal list of generating relations of a poset
• coxeterPolynomial -- computes the Coxeter polynomial of a poset
• diamondProduct -- computes the diamond product of two ranked posets
• dilworthLattice -- computes the Dilworth lattice of a poset
• dilworthNumber -- computes the Dilworth number of a poset
• displayPoset -- generates a PDF representation of a poset and attempts to display it
• distributiveLattice -- computes the lattice of order ideals of a poset
• divisorPoset -- generates the poset of divisors
• divisorPoset(List,List,PolynomialRing) -- generates the poset of divisors
• divisorPoset(RingElement) -- generates the poset of divisors
• divisorPoset(RingElement,RingElement) -- generates the poset of divisors with a lower and upper bound
• dominanceLattice -- generates the dominance lattice of partitions of $n$
• dropElements -- computes the induced subposet of a poset given a list of elements to remove
• dual(Poset) -- produces the derived poset with relations reversed
• Example: Constructing common posets
• Example: Hibi ideals
• Example: Intersection lattices
• Example: LCM-lattices
• facePoset -- generates the face poset of a simplicial complex
• filter -- computes the elements above given elements in a poset
• filtration -- generates the filtration of a poset
• flagChains -- computes the maximal chains in a list of flags of a ranked poset
• flagfPolynomial -- computes the flag-f polynomial of a ranked poset
• flaghPolynomial -- computes the flag-h polynomial of a ranked poset
• flagPoset -- computes the subposet of specified ranks of a ranked poset
• fPolynomial -- computes the f-polynomial of a poset
• gapConvertPoset -- converts between Macaulay2's Posets and GAP's Posets
• greeneKleitmanPartition -- computes the Greene-Kleitman partition of a poset
• hasseDiagram -- produces the Hasse diagram of a poset
• height(Poset) -- computes the height of a poset
• hibiIdeal -- produces the Hibi ideal of a poset
• hibiRing -- produces the Hibi ring of a poset
• hPolynomial -- computes the h-polynomial of a poset
• incomparabilityGraph -- produces the incomparability graph of a poset
• indexLabeling -- relabels a poset with the labeling based on the indices of the vertices
• intersectionLattice -- generates the intersection lattice of a hyperplane arrangement
• isAntichain -- determines if a given list of vertices is an antichain of a poset
• isAtomic -- determines if a lattice is atomic
• isBounded -- determines if a poset is bounded
• isComparabilityGraph -- determines if a graph is the comparability graph of a poset
• isConnected(Poset) -- determines if a poset is connected
• isDistributive -- determines if a lattice is distributive
• isEulerian(Poset) -- determines if a ranked poset is Eulerian
• isGeometric -- determines if a lattice is geometric
• isGraded -- determines if a poset is graded
• isLattice -- determines if a poset is a lattice
• isLowerSemilattice -- determines if a poset is a lower (or meet) semilattice
• isLowerSemimodular -- determines if a ranked lattice is lower semimodular
• isModular -- determines if a lattice is modular
• isomorphism -- computes an isomorphism between isomorphic posets
• isRanked -- determines if a poset is ranked
• isSperner -- determines if a ranked poset has the Sperner property
• isStrictSperner -- determines if a ranked poset has the strict Sperner property
• isUpperSemilattice -- determines if a poset is an upper (or join) semilattice
• isUpperSemimodular -- determines if a lattice is upper semimodular
• joinExists -- determines if the join exists for two elements of a poset
• joinIrreducibles -- determines the join irreducible elements of a poset
• labelPoset -- relabels a poset with the specified labeling
• lcmLattice -- generates the lattice of lcms in an ideal
• linearExtensions -- computes all linear extensions of a poset
• maximalAntichains -- computes all maximal antichains of a poset
• maximalChains -- computes all maximal chains of a poset
• maximalElements -- determines the maximal elements of a poset
• meetExists -- determines if the meet exists for two elements of a poset
• meetIrreducibles -- determines the meet irreducible elements of a poset
• minimalElements -- determines the minimal elements of a poset
• moebiusFunction -- computes the Moebius function at every pair of elements of a poset
• naturalLabeling -- relabels a poset with a natural labeling
• ncPartitions -- generates the non-crossing partitions of size $n$
• ncpLattice -- computes the non-crossing partition lattice of set-partitions of size $n$
• openInterval -- computes the subposet contained strictly between two points
• orderComplex -- produces the order complex of a poset
• orderIdeal -- computes the elements below given elements in a poset
• outputTexPoset -- writes a LaTeX file with a TikZ-representation of a poset
• partitionLattice -- computes the lattice of set-partitions of size $n$
• plueckerPoset -- computes a poset associated to the Plücker relations
• poincarePolynomial -- computes the Poincare polynomial of a ranked poset with a unique minimal element
• Poset -- a class for partially ordered sets (posets)
• poset -- creates a new Poset object
• Poset _ List -- returns elements of the ground set
• Poset _ ZZ -- returns an element of the ground set
• Poset _* -- returns the ground set of a poset
• posetJoin -- determines the join for two elements of a poset
• posetMeet -- determines the meet for two elements of a poset
• pPartitionRing -- produces the p-partition ring of a poset
• Precompute -- a package-wide configuration that toggles precomputation
• principalFilter -- computes the elements above a given element in a poset
• principalOrderIdeal -- computes the elements below a given element in a poset
• product(Poset,Poset) -- computes the product of two posets
• projectivizeArrangement -- computes the intersection poset of a projectivized hyperplane arrangement
• randomPoset -- generates a random poset with a given relation probability
• rankFunction -- computes the rank function of a ranked poset
• rankGeneratingFunction -- computes the rank generating function of a ranked poset
• rankPoset -- generates a list of lists representing the ranks of a ranked poset
• realRegions -- computes the number of regions a hyperplane arrangement divides the space into
• removeIsomorphicPosets -- returns a sub-list of non-isomorphic posets
• resolutionPoset -- generates a poset from a resolution
• setPartition -- computes the list of set-partitions of size $n$
• setPrecompute -- sets the Precompute configuration
• setSuppressLabels -- sets the SuppressLabels configuration
• standardMonomialPoset -- generates the poset of divisibility in the monomial basis of an ideal
• subposet -- computes the induced subposet of a poset given a list of elements
• texPoset -- generates a string containing a TikZ-figure of a poset
• transitiveClosure -- computes the transitive closure of a set of relations
• transitiveOrientation -- generates a poset whose comparability graph is the given graph
• tuttePolynomial -- computes the Tutte polynomial of a poset
• union -- computes the union of two posets
• youngSubposet -- generates a subposet of Young's lattice
• zetaPolynomial -- computes the zeta polynomial of a poset