Proceedings of the 28-th International Conference on Formal Power Series and Algebraic Combinatorics
4-8 Jul 2016 Vancouver, British Columbia (Canada)

Extended abstracts listed by author > Rinaldi Simone

Slicings of parallelogram polyominoes, or how Baxter and Schro ̈der can be reconciled
Mathilde Bouvel  1  , Veronica Guerrini  2  , Simone Rinaldi  2  
1 : Institut für Mathematik [Zürich]  -  Website
Winterthurerstrasse 190, CH-8057 Zürich -  Suisse
2 : Dipartimento di Ingegneria dellínformazione e scienze matematiche [Siena]  (DIISM)  -  Website
San Niccolò, via Roma, 56 53100 Siena -  Italie

We provide a new succession rule (i.e. generating tree) associated with Schro ̈der numbers, that interpolates between the known succession rules for Catalan and Baxter numbers. We define Schro ̈der and Baxter generalizations of parallelogram polyominoes (called slicings) which grow according to these succession rules. We also exhibit Schro ̈der subclasses of Baxter classes, namely a Schro ̈der subset of triples of non-intersecting lattice paths, and a new Schro ̈der subset of Baxter permutations. 

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