Hi Bruce,
> Just to clarify; I refer to tableaux because I am taking constructions
> that are well know for tableaux
> and generalising. One example is oscillating tableaux; these are sequences
> of partitions where you
> add or remove a single box at each step. One example I want to experiment
> with is vacillating tableaux.
> Then we have alternating tableaux, ribbon tableaux, ...
>
Just a comment about the object that you are proposing to work with.
Vascillating tableaux are in bijection with set valued tableaux and that
might be a simpler object to work with and manipulate in sage (because you
could represent it as a pair of a standard tableau and a list of sets).
For example the vascillating tableaux of semi-length 2 and size 5 are:
((5), (4), (5), (4), (5))
((5), (4), (4,1), (4), (5))
((5), (4), (5), (4), (4,1))
((5), (4), (4,1), (4), (4,1))
((5), (4), (4,1), (3,1), (4,1))
((5), (4), (4,1), (3,1), (3,2))
((5), (4), (4,1), (3,1), (3,1,1))
[[.,.,.,.,12]]
[[.,.,.,1,2]]
[[.,.,.,1],[2]]
[[.,.,.,2],[1]]
[[.,.,.,.],[12]]
[[.,.,.],[1,2]]
[[.,.,.],[1],[2]]
The reason I mention this is because I have written code to work with set
valued tableaux. It isn't super robust because I kept changing
conventions, but if you want to try it out, copy or modify it, I put it on
a web page. This way you can load it by executing the commands (or just
view the code by following the links):
load("http://garsia.math.yorku.ca/~zabrocki/multisetpartition.py";)
load("http://garsia.math.yorku.ca/~zabrocki/multisettableau.py";)
-Mike
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