Slicings of parallelogram polyominoes, or how Baxter and Schro ̈der can be reconciled
We provide a new succession rule (i.e. generating tree) associated with Schro ̈der numbers, that interpolates between the known succession rules for Catalan and Baxter numbers. We define Schro ̈der and Baxter generalizations of parallelogram polyominoes (called slicings) which grow according to these succession rules. We also exhibit Schro ̈der subclasses of Baxter classes, namely a Schro ̈der subset of triples of non-intersecting lattice paths, and a new Schro ̈der subset of Baxter permutations.
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| Thématiques | : | |
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