Code

Sage Scripts

• vertex_decomposability.sage - provides functions to check whether a given simplicial complex is vertex decomposable.
• parabolic_cataland.zip - provides functions to construct parabolic Tamari lattices and related objects. (Accompanies my article on parabolic Tamari lattices.)
• hurwitz.sage - provides functions to create factorization posets and deduce Hurwitz orbits in generated groups. (Accompanies my article with V. Ripoll on connectivity of factorization posets.)
• sperner.sage - provides functions to import noncrossing partition lattices to Sage, and some test routines revolving around the Sperner property. (Accompanies my article on symmetric decompositions of noncrossing partition lattices.)
• m_tamari_decomposition.sage - provides functions to perform the strip decomposition of m-Dyck paths, and some test routines revolving around a conjecture that the m-Tamari lattice of parameter n is isomorphic to a modification of the poset of strip-decomposed m-Dyck paths under componentwise rotation order. (Accompanies my article with M. Kallipoliti on m-cover posets.)

Gap3 Scripts

• print_nc.gap - provides functions to print the cover relations in a noncrossing partition lattice associated with any irreducible well-generated complex reflection group.

Some Lattice Repositories

• ncp.zip - this is an archive containing a few noncrossing partition lattices. More precisely, the files in this archive contain the cover relations of these lattices. So far, I have included all noncrossing partition lattices associated with:
  • real reflection groups of rank at most 8,
  • irreducible well-generated exceptional non-real complex reflection groups,
  • the groups G(d,d,n) for 3 ≤ d ≤ 8 and 3 ≤ n ≤ 6, as well as 3 ≤ d ≤ 6 and n=7.
• lattices.zip - this is an archive containing certain families of lattices. So far, I have included all:
  • distributive lattices of size ≤18
  • congruence-uniform lattices of size ≤13
  • extremal lattices of size ≤12
  • left-modular lattices of size ≤12
  • trim lattices of size ≤12
  • join-semidistributive lattices of size ≤12

This archive also contains a script called init.sage that allows for importing these lattices into Sage. Just load said script into Sage, and call the function load_all(type), where the parameter 'type' may be either one of: 'distributive', 'congruence_uniform', 'extremal', left_modular', 'trim', 'join_semidistributive', depending on which class of lattices you want to load. This function returns a dictionary that maps an integer to a list of all lattices of this cardinality. (Of course only if the lattices of the requested type and cardinality are contained in the archive.)