Posets -- a package for working with partially ordered sets
Description
This package defines Poset as a new data type and provides routines which use or produce posets. A poset (partially ordered set) is a set together with a binary relation satisfying reflexivity, antisymmetry, and transitivity.
A few methods in this package have been ported from John Stembridge’s Maple package implementing posets, which is available at http://www.math.lsa.umich.edu/~jrs/maple.html#posets. Such methods are noted both in the source code and in the documentation.
youngSubposet -- generates a subposet of Young's lattice
zetaPolynomial -- computes the zeta polynomial of a poset
Methods
adjoinMax(Poset), see adjoinMax -- computes the poset with a new maximum element
adjoinMax(Poset,Thing), see adjoinMax -- computes the poset with a new maximum element
adjoinMin(Poset), see adjoinMin -- computes the poset with a new minimum element
adjoinMin(Poset,Thing), see adjoinMin -- computes the poset with a new minimum element
allRelations(Poset), see allRelations -- computes all relations of a poset
allRelations(Poset,Boolean), see allRelations -- computes all relations of a poset
antichains(Poset), see antichains -- computes all antichains of a poset
antichains(Poset,ZZ), see antichains -- computes all antichains of a poset
areIsomorphic(Poset,Poset), see areIsomorphic -- determines if two posets are isomorphic
Poset == Poset, see areIsomorphic -- determines if two posets are isomorphic
atoms(Poset), see atoms -- computes the list of elements covering the minimal elements of a poset
augmentPoset(Poset), see augmentPoset -- computes the poset with an adjoined minimum and maximum
augmentPoset(Poset,Thing,Thing), see augmentPoset -- computes the poset with an adjoined minimum and maximum
chains(Poset), see chains -- computes all chains of a poset
chains(Poset,ZZ), see chains -- computes all chains of a poset
characteristicPolynomial(Poset), see characteristicPolynomial -- computes the characteristic polynomial of a ranked poset with a unique minimal element
closedInterval(Poset,Thing,Thing), see closedInterval -- computes the subposet contained between two points
comparabilityGraph(Poset), see comparabilityGraph -- produces the comparability graph of a poset
compare(Poset,Thing,Thing), see compare -- compares two elements in a poset