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Published online by Cambridge University Press: 05 June 2012
In this appendix we discuss a few of the many variations on the themes of Part I. Several of these give alternative constructions of the product of tableaux. Others give new versions of the Littlewood–Richardson correspondences. Still others describe “dual” versions of notions from Part I. They are included to tie together a variety of approaches and results in the literature, and to illustrate the richness of the combinatorics of tableaux (or at least this author's inability to resist the temptation). The reader may use them as a source of exercises for Part I.
In this appendix we follow the “compass” conventions introduced in §4.2.
Dual alphabets and tableaux
A first construction, which seems best qualified for the designation “duality,” is one that, in the language of words, replaces each word by a word in a dual or opposite alphabet. On tableaux, this corresponds to a construction using the reverse sliding algorithm, sometimes called “evacuation.”
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