Posets_(IMA2011)

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title: Posets (IMA2011) permalink: wiki/Posets_(IMA2011)/ layout: wiki

Useful links

• Function list for Stembridge's Posets Package
• Curtis Greene package
• Stanley's Enumerative Combinatorics, Volume 1

David's to do list

• For all enumerated/derived posets, add precomputed easy properties. (E.g., chain's are graded and ranked with an easy ranking functions.)
• Write tests and documentation

Sonja's to do list

• Write tests and documentation
• [Sonja: Do you have any methods you would like to implement (or see implemented--I'm happy to help)?]

Gwyn's to do list

• partitionLattice, nonCrossingPartitionLattice, nonCrossingPairingLattice
• (28. July 2011) Zach Teitler asked for the intersection lattice of a hyperplane arrangement and subspace arrangement lattice
• (29. July 2011) Zach Teitler asked for the minimal building sets of an intersection lattice (indecomposible elements) and tests for isIndecomposible.
• Write tests and documentation

Suggestions

From Vic Reiner on 26. July 2011 for:

• Posets:
  • all linear extensions of P
  • compute the rank-generating-function if ranked
  • the Greene-Kleitman partition \lambda(P)
  • Hibi ring Hibi ring presentation
  • P-partition ring p-Partition presentation
  • given a graph, identify if it is a comparability graph (see GoogleBooks)
  • examine Curtis Greene package for additional Poset libraries
• SimplicialComplexesPlus:
  • implement simplicial maps
  • cup products, cohomology operations (Posets or simplicial complexes)
  • better algorithms for clique complexes of graphs

Simplicial Complexes Plus

• Integral homology via GAP interface

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