Geodesic
Slicings of parallelogram polyominoes, or how Baxter and Schröder can be reconciled
Discrete mathematics & theoretical computer science, DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016), DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016) (2020) Cet article a éte moissonné depuis la source Episciences

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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. 
@article{DMTCS_2020_special_379_a39,
     author = {Bouvel, Mathilde and Guerrini, Veronica and Rinaldi, Simone},
     title = {Slicings of parallelogram polyominoes, or how {Baxter} and {Schr\"oder} can be reconciled},
     journal = {Discrete mathematics & theoretical computer science},
     year = {2020},
     volume = {DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016)},
     doi = {10.46298/dmtcs.6357},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.6357/}
}
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VL  - DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016)
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%T Slicings of parallelogram polyominoes, or how Baxter and Schröder can be reconciled
%J Discrete mathematics & theoretical computer science
%D 2020
%V DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016)
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%F DMTCS_2020_special_379_a39
Bouvel, Mathilde; Guerrini, Veronica; Rinaldi, Simone. Slicings of parallelogram polyominoes, or how Baxter and Schröder can be reconciled. Discrete mathematics & theoretical computer science, DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016), DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016) (2020). doi: 10.46298/dmtcs.6357

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