I actually started a project like this a while back. I made a catalog which accepts generators and mappings, and constructs mappings between objects types you've connected. It does some plotting, too.
One weird thing about it is that I use the labels from Richard Stanley's catalog of objects. balanced parentheses dyck paths coin stacks noncrossing matchings permutations avoiding 231, 132, 312, 213 noncrossing partitions nonnesting matchings binary trees http://sagenb.org/home/pub/4609/ On Sat, Mar 24, 2012 at 11:31 AM, Christian Stump <christian.st...@gmail.com> wrote: > Hi there, > >> it would be great if you worked on that. some of it has already be >> done in the patch trac_11571_catalan_objects-nm.patch > > if I see it right, there are currently implemented > > - Dyck paths > - Motzkin paths (which are not really counted by Catalan) > > in this folder. I don't know how much people work on getting > "classical" Catalan combinatorics into Sage - is there more than Dyck > paths currently? > > In the past, I implemented various objects that are counted by > Coxeter-Catalan numbers which are numbers associated to finite > reflection groups such that we get back the classical Catalan numbers > when looking at the symmetric group. See e.g. Section 1.1. in > http://arxiv.org/abs/math/0611106. > > Here is a not necessarily exhaustive list (with the classical > corresponding object in brackets). > > - facets in the cluster complex (triangulations of a multi-gon), > - Coxeter-sortable elements (231-pattern avoiding permutations), > - noncrossing partitions (noncrossing set partitions), > - facets in a certain "subword complex" (triangulations), > - antichains in the root poset (Dyck paths), > - vertices of the generalized associahedron > > I have also implementations of bijections between all of them except > antichains in the root poset. The reason is that all the others are > naturally connected in a type-free way, while antichains in the root > poset were connected in http://arxiv.org/abs/1101.1277, but I have not > had the time to implement this bijection (which is inductively defined > in a subtle way and thus not easy to implement). > > I will be thinking about that in the next days and if people agree I > will turn #11571 into an overview patch on what (Coxeter-)Catalan > objects and bijections we have. > > I would also be very interested in people working on the classical > situation to get objects like triangulations into sage (+1 for nice > drawings as well, see my macros in tikz for that, > http://homepage.univie.ac.at/christian.stump/code.html). If we have > (or if we are going to have) any objects implemented, I will be happy > to provide bijections from the Coxeter-Catalan setting to the concrete > implementation for the symmetric group. > > If you need any help on how to work on that, let me know! > > Best, Christian > > -- > You received this message because you are subscribed to the Google Groups > "sage-combinat-devel" group. > To post to this group, send email to sage-combinat-devel@googlegroups.com. > To unsubscribe from this group, send email to > sage-combinat-devel+unsubscr...@googlegroups.com. > For more options, visit this group at > http://groups.google.com/group/sage-combinat-devel?hl=en. > -- You received this message because you are subscribed to the Google Groups "sage-combinat-devel" group. To post to this group, send email to sage-combinat-devel@googlegroups.com. To unsubscribe from this group, send email to sage-combinat-devel+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/sage-combinat-devel?hl=en.
