Abstract
We present a bijection between balanced Delannoy paths of length 2n and the faces of the n-dimensional Simion type B associahedron. This polytope is also known as the Bott-Taubes polytope and the cyclohedron. This bijection takes a path with k up steps (and k down steps) to a (k − 1)-dimensional face of the Simion type B associahedron. We give two presentations of this bijection, one recursive and one non-recursive.
| Original language | English |
|---|---|
| Article number | 19.1.2 |
| Journal | Journal of Integer Sequences |
| Volume | 22 |
| Issue number | 1 |
| State | Published - 2019 |
Bibliographical note
Publisher Copyright:© 2019, University of Waterloo. All rights reserved.
Funding
We would like to thank the referee for helping substantially improve the presentation. The first and third author thank the Institute for Advanced Study in Princeton, New Jersey, for a research visit in Summer 2018. This work was partially supported by grants from the Simons Foundation (#429370 to Richard Ehrenborg, #245153 and #514648 to Gábor Hetyei, #206001 and #422467 to Margaret Readdy).
| Funders | Funder number |
|---|---|
| Simons Foundation | 422467, 206001, 429370, 514648, 245153 |
Keywords
- Bott-Taubes polytope
- Delannoy number
- F-vector
- Schröder path
- Type B associahedron
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics