We introduce the notions of Schröder shape and of Schröder tableau, which provide some kind of analogs of the classical notions of Young shape and Young tableau. We investigate some properties of the partial order given by containment of Schröder shapes. Then we propose an algorithm which 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 Schröder tableau with those of interval order and of weak containment (and strong avoidance) of posets. We end our paper with several suggestions for possible further work.
Schröder partitions, Schröder tableaux and weak poset patterns / Luca Ferrari. - In: CONTRIBUTIONS TO DISCRETE MATHEMATICS. - ISSN 1715-0868. - ELETTRONICO. - 16:(2021), pp. 160-184. [10.11575/cdm.v16i1.62653]
Schröder partitions, Schröder tableaux and weak poset patterns
Luca Ferrari
2021
Abstract
We introduce the notions of Schröder shape and of Schröder tableau, which provide some kind of analogs of the classical notions of Young shape and Young tableau. We investigate some properties of the partial order given by containment of Schröder shapes. Then we propose an algorithm which 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 Schröder tableau with those of interval order and of weak containment (and strong avoidance) of posets. We end our paper with several suggestions for possible further work.File | Dimensione | Formato | |
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