Posets_and_Combinatorial_CA

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title: Posets and Combinatorial CA permalink: wiki/Posets_and_Combinatorial_CA/ layout: wiki

Work to be done on MonomialIdealResolutions package:

• fix scarf function
• missing documentation/figure out what exactly the functions missing documentation are doing
• missing tests

Functions we'd like to add to MonomialIdealResolutions package:

• isScarf
• isRigid
• more resolution constructions that perhaps use the lcm-lattice such as poset resolution or Lyubeznik resolution
• functions related to splittings (if they are not already in edge ideals)
• change the current isGenericMonIdeal to isStronglyGeneric, and add a new isGenericMonIdeal that checks the generic condition in the Miller, Sturmfels, Yanagawa paper
• add functions dealing with deformation of exponents

Work to be done on posets package:

• note "bug" in union page of posets documentation
• figure out the status of the graphs package and make sure that the two packages are interacting nicely
• add functions which test things like order preserving-ness, join preserving-ness, etc for maps on the groundsets of posets and maybe some stuff relating to the fiber theorems
• optimize intersection lattice
• add tests
• crosscut complex, identify crosscuts
• change documentation on isAtomic to reflect that it is actually returning an answer to isAtomicLattice, write function that finds support in atoms for elements in finite atomic lattice
• make posets know their own name and fix all net issues

Work to be done on Permutations package:

• Fix simple transpositions code - see if it correctly eliminates duplicates.
• Revisit code, check whether various constructors work properly.
• Examine Bruhat/weak-Bruhat orders, verify correct outputs.

Work to be done on SimplicialComplexesPlus package:

Work to be done on Graphs package:

• Add documentation to new functions (reverseDigraph, reverseEdge)
• Repair tex code for graphs, distinguish between "ranked" digraph and "unranked" digraph.