Abstract
We introduce the notions of Schroder shapes and Schroder tableaux, which provide an analog of the classical notions of Young shapes and Young tableaux. We investigate some properties of the partial order given by containment of Schroder shapes. Then we propose an algorithm that is the natural analog of the well-known RS correspondence for Young tableaux, and we characterize those permutations whose insertion tableaux have some special shapes. The last part of the article relates the notion of the Schroder tableau with those of interval order and weak containment (and strong avoidance) of posets. We end our paper with several suggestions for possible further work.
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