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- W3000071903 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 $m$-row-restricted slicings, for $m in mathbb{N}$. Using functional equations and the kernel method, their generating functions are computed in some special cases, and we conjecture that they are algebraic for any $m$." @default.
- W3000071903 created "2020-01-23" @default.
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- W3000071903 date "2019-07-19" @default.
- W3000071903 modified "2023-09-30" @default.
- W3000071903 title "Slicings of Parallelogram Polyominoes: Catalan, Schröder, Baxter, and Other Sequences" @default.
- W3000071903 doi "https://doi.org/10.37236/7375" @default.
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