Name
Title | ||
|---|---|---|
Slicings of Parallelogram Polyominoes: Catalan, Schröder, Baxter, and Other Sequences. |
Abstract | ||
|---|---|---|
We provide a new succession rule (i.e. generating tree) associated with Schroder numbers, that interpolates between the known succession rules for Catalan and Baxter numbers. We define Schroder and Baxter generalizations of parallelogram polyominoes, called slicings, which grow according to these succession rules. In passing, we also exhibit Schroder subclasses of Baxter classes, namely a Schroder subset of triples of non-intersecting lattice paths, a new Schroder subset of Baxter permutations, and a new Schroder 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 is an element of 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. |
Year | Venue | Keywords |
|---|---|---|
2019 | ELECTRONIC JOURNAL OF COMBINATORICS | Parallelogram polyominoes,Generating trees,Baxter numbers,Schroder numbers,Catalan numbers,Non-intersecting lattice paths,Kernel method |
DocType | Volume | Issue |
Journal | 26 | 3 |
ISSN | Citations | PageRank |
1077-8926 | 0 | 0.34 |
References | Authors | |
0 | 4 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Nicholas R. Beaton | 1 | 3 | 2.14 |
| Mathilde Bouvel | 2 | 64 | 9.64 |
| Veronica Guerrini | 3 | 0 | 0.34 |
| Simone Rinaldi | 4 | 174 | 24.93 |