# Tableau Diagrams

I just finished writing a complicated bit of combinatorics involving signed quasi-bipartitions for a paper I’m working on. Part of the proof relies on a simultaneous degeneration of two bipartitions which are subordinate to a pair of signed quasi-bipartitions. The diagram to explain part of that argument is pretty involved:

The layout and arrows in the diagram are handled by the XY package (xymatrix) in latex whereas the tableaux are drawn by a complicated latex macro, borrowed from my collaborators and extended in a few ways to produce the figures needed.

By the way, tableau is a French diminutive for “table” and tableaux is it’s plural.

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You have been teasing me with your diagrams for several days. What is the most elementary text available to better understand what you are doing.

Thanks, connie

Connie- That’s a good question. It depends on what “elementary” means I guess. There’s a discussion of tableau in representation theory at http://en.wikipedia.org/wiki/Young_tableau . In the paper I’m writing the diagrams are related to nilpotent operators in finite dimensional vector spaces. Probably the best reference for this is “Nilpotent orbits and Representation Theory” by Jens Jantzen. Both of these references are probably graduate level or beyond.

BrunoJ

Thanks for the swift response. My last math class was diffeq. Looked at the Wikipedia entry, good way to get started, and can see the subject gets deep and steep rapidly.

Thanks again for the help, connie