Slicings of parallelogram polyominoes: Catalan, Schr\"oder, Baxter, and other sequences

@inproceedings{Beaton2015SlicingsOP,
  title={Slicings of parallelogram polyominoes: Catalan, Schr\"oder, Baxter, and other sequences},
  author={Nicholas R. Beaton and Mathilde Bouvel and Veronica Guerrini and Simone Rinaldi},
  year={2015}
}
We provide a new succession rule (i.e. generating tree) associated with Schr\"oder numbers, that interpolates between the known succession rules for Catalan and Baxter numbers. We define Schr\"oder and Baxter generalizations of parallelogram polyominoes, called slicings, which grow according to these succession rules. In passing, we also exhibit Schr\"oder subclasses of Baxter classes, namely a Schr\"oder subset of triples of non-intersecting lattice paths, a new Schr\"oder subset of Baxter… CONTINUE READING

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