This is intriguing but I need some help as I am not familiar with these.
Can you give me some references on the background?

In my setup, a "tableau" is a sequence of "partitions" with constraints
on neighbouring partitions. Do set valued tableaux, or multiset valued 
tableaux,
fit this framework?

P.S. Are you planning on submitting this code to sage? It seems that you
should, particularly as it is now in the public domain.

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