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.
|Journal||Journal of Integer Sequences|
|State||Published - 2019|
Bibliographical noteFunding Information:
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).
© 2019, University of Waterloo. All rights reserved.
- Bott-Taubes polytope
- Delannoy number
- Schröder path
- Type B associahedron
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics