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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.

Acknowledgement

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.

Citation

If you have used this package in your research, please cite it as follows:

@misc{SimplicialPosetsSource,
  title = {{SimplicialPosets: constructing Stanley simplicial poset rings. Version~1.0}},
  author = {Nathan Nichols},
  howpublished = {A \emph{Macaulay2} package available at
    \url{https://github.com/Macaulay2/M2/tree/master/M2/Macaulay2/packages}}
}

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, defined in SimplicialPosets.m2.

The source of this document is in SimplicialPosets.m2:254:0.