Yes, this was suggested to me after I'd abandoned the catalog I
posted. I'm fairly sure that most, if not all of my bijections follow
directly from the recursive structure of Catalan objects.
On Mon, Mar 26, 2012 at 10:25 AM, matthew Drescher <knav...@gmail.com> wrote:
> i would be interested. I had it in mind to focus on the recursive structure
> of the Catalan objects( objects that can be counted via catalan numbers).
>
> C_{n+1} = \sum_{i=0}^{n}C_{n-i}C_{i}
>
> when defining a new catalan object we would just need to specify the
> recursive structure. This way we might not have to deal with specific
> bijections....but that was just my initial idea...i dont know :)
>
>
>
> On Mon, Mar 26, 2012 at 9:54 AM, Christian Stump <christian.st...@gmail.com>
> wrote:
>>
>> > Christian, this is far from standard. It's fairly discombobulated
>> > scratch work. The objects aren't even classes.
>>
>> my last reply was too fast, sorry. Now as I look at the actual code, I
>> see what you are doing... Nonetheless, I find it a nice idea to gather
>> Catalan objects and their bijections, as people are apparently looking
>> for that!
>>
>> What about implementing the objects as classes in the folder
>> combinat/catalan (maybe with some identifications by "canonical
>> bijections", like i = h = zzzz = r = hhh), and then making them
>> available as
>>
>> CatalanObjects.YourCatalanObject
>>
>> like in
>>
>> Posets.BooleanLattice
>>
>> (to not pollute the global name space too much), and also provide
>> bijections, maybe in
>>
>> CatalanObjects.Bijections.YourFavoriteBijection
>>
>> (these are, of course, not unique, so we must give them names to
>> distinguish, like "reverse" and "upside-down" to get from
>> \sigma-avoiding permutations to reverse(\sigma)-avoiding permutations
>> for \sigma \in S_3.)
>>
>> Better or other ideas, suggestions?
>>
>> @vivace: are you interested in working/collaborating on that? was this
>> somehow what you thought of?
>>
>> cheers, Christian
>>
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