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SimplicialPosets :: SimplicialPosets

SimplicialPosets -- A package for working with simplicial posets.

Description

The primary purpose of this package is to implement the simplicial poset ring as defined by Richard P. Stanley in 1989.

Stanley's original paper.

Acknowledgements:

This package uses some code from the Posets package.

Thanks to Victor Reiner. This project was his idea.

Author

Version

This documentation describes version 1.0 of SimplicialPosets.

Source code

The source code from which this documentation is derived is in the file SimplicialPosets.m2.

Exports

  • Functions and commands
    • fromFVector -- If possible, returns a simplicial poset with the given f-vector.
    • getFVector -- Returns the f-vector {f_{-1},f_0,...,f_{d-1}} of the given poset.
    • isBoolean -- Determine if a poset is a boolean algebra.
    • stanleyPosetIdeal -- Returns ideal that defines the simplicial poset ring of the given simplicial poset.
    • testFVector -- Tests if it is possible for a simplicial poset to have a given f-vector.
  • Methods
    • "fromFVector(List)" -- see fromFVector -- If possible, returns a simplicial poset with the given f-vector.
    • "getFVector(Poset)" -- see getFVector -- Returns the f-vector {f_{-1},f_0,...,f_{d-1}} of the given poset.
    • "isBoolean(Poset)" -- see isBoolean -- Determine if a poset is a boolean algebra.
    • "isSimplicial(Poset)" -- see isSimplicial -- Determine if a poset is simplicial.
    • "stanleyPosetIdeal(Poset)" -- see stanleyPosetIdeal -- Returns ideal that defines the simplicial poset ring of the given simplicial poset.
    • "testFVector(List)" -- see testFVector -- Tests if it is possible for a simplicial poset to have a given f-vector.

For the programmer

The object SimplicialPosets is a package.