Slicings of parallelogram polyominoes, or how Baxter and Schröder can be reconciled

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 su...

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Vydáno v:	Discrete mathematics and theoretical computer science Ročník DMTCS Proceedings, 28th...
Hlavní autoři:	Bouvel, Mathilde, Guerrini, Veronica, Rinaldi, Simone
Médium:	Journal Article Konferenční příspěvek
Jazyk:	angličtina
Vydáno:	DMTCS 22.04.2020 Discrete Mathematics & Theoretical Computer Science
Témata:	[math.math-co]mathematics [math]/combinatorics [math.co] Combinatorics Mathematics
ISSN:	1365-8050, 1462-7264, 1365-8050
On-line přístup:	Získat plný text
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Popis
Shrnutí:	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.
ISSN:	1365-8050 1462-7264 1365-8050
DOI:	10.46298/dmtcs.6357