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An analogue of the plactic monoid for binary search trees. (Un analogue du monoïde plaxique pour les arbres binaires de recherche.) (French) Zbl 1013.05026
Summary: We introduce a monoid structure on a certain set of labelled binary trees, by a process similar to the construction of the plactic monoid. This leads to a new interpretation of the algebra of planar binary trees of J.-L. Loday and M. O. Ronco [Adv. Math. 139, 293-309 (1998; Zbl 0926.16032) and J. Algebr. Comb. 15, 253-270 (2002; Zbl 0998.05013)].

MSC:
05C05 Trees
68R10 Graph theory (including graph drawing) in computer science
68P10 Searching and sorting
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