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Slicings of parallelogram polyominoes, or how Baxter and Schröder can be reconciled

Type of publication Peer-reviewed
Publikationsform Proceedings (peer-reviewed)
Author Bouvel Mathilde, Guerrini Veronica, Rinaldi Simone,
Project Permutation classes: from structure to combinatorial properties
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Proceedings (peer-reviewed)

Title of proceedings FPSAC 2016
Place Vancouver, Canada

Open Access

Type of Open Access Website


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