Mathilde Bouvel ; Veronica Guerrini ; Simone Rinaldi - Slicings of parallelogram polyominoes, or how Baxter and Schröder can be reconciled

dmtcs:6357 - Discrete Mathematics & Theoretical Computer Science, April 22, 2020, DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016) - https://doi.org/10.46298/dmtcs.6357
Slicings of parallelogram polyominoes, or how Baxter and Schröder can be reconciledArticle

Authors: Mathilde Bouvel 1; Veronica Guerrini 2; Simone Rinaldi 2

  • 1 Institut für Mathematik [Zürich]
  • 2 Dipartimento di Ingegneria dell'informazione e scienze matematiche [Siena]

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.

https://doi.org/10.46298/dmtcs.6357
Source: HAL:hal-02173392v1
Volume: DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016)
Published on: April 22, 2020
Imported on: July 4, 2016
Keywords: [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]
Funding:
    Source : OpenAIRE Graph
  • Permutation classes: from structure to combinatorial properties; Funder: Swiss National Science Foundation; Code: 151254

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