Journal article

Slicings of parallelogram polyominoes: Catalan, Schroder, Baxter, and other sequences

Nicholas R Beaton, Mathilde Bouvel, Veronica Guerrini, Simone Rinaldi

ELECTRONIC JOURNAL OF COMBINATORICS | ELECTRONIC JOURNAL OF COMBINATORICS | Published : 2019

Abstract

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. In passing, we also exhibit Schröder subclasses of Baxter classes, namely a Schröder subset of triples of non-intersecting lattice paths, a new Schröder subset of Baxter permutations, and a new Schröder subset of mosaic floorplans. Finally, we define two families of subclasses of Baxter slicings: the m-skinny slicings and the m-rowrestricted slicings, for m ∈ N. Using functional eq..

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University of Melbourne Researchers

Grants

Awarded by Australian Research Council


Funding Acknowledgements

The first author was supported by the Pacific Institute for the Mathematical Sciences and in particular the Collaborative Research Group in Applied Combinatorics, and the Australian Research Council grant DE170100186.