Elsevier, Discrete Mathematics, 1-3(99), p. 115-122, 1992
DOI: 10.1016/0012-365x(92)90369-q
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This is a sequel to the first author's paper ‘Dual equivalence with applications, including a conjecture of Proctor.’ One result of that paper is that certain shifted and unshifted shapes (the generalized staircases) have the property that Schützenberger's total promotion operator acts as the identify or the transpose. Here we prove that generalized staircases are essentially the only shapes with these promotion properties.