Release
May 2006: lcell version 0.2.
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Latest News
May 2005: Release of lcell version 0.2: available for all platforms with Python support.
May 2005: Release of lcell version 0.1: available for all platforms with Python support.
Overview of lcell
lcell generates the distributive lattice representing all linear extensions of a given partial order. This lattice also represents a cell in an order subdivision, which can, for example, be induced by a weight vector or DSG axioms. Further it can answer certain questions about this structure.
The main algorithm was created according to ideas developed by Anne Shiu, Jason Morton and Oliver Wienand.
Main computational objects:
- Linear extensions of a partial order, represented as a distributive lattice.
Input objects:
- A partial order as a cover relation.
- A set of DSG axioms.
- A weight vector or its moebius transform.
- A distributive lattive via its vertex list.
- A list of data vectors, which pairwise comparisons generates a the partial order.
Available computations (excerpt):
- Number of linear extensions of a partial order, i.e. the number of maximal chains in a cell.
- All linear extensions in form of a distributive lattice.
- A cover relation for a cell in a subdivision, readable by the MAPLE posets package from XXX.
lcell is free software under the revised BSD license.
lcell is developed by Oliver Wienand.