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 |
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Article number | 19.1.2 |
Journal | Journal of Integer Sequences |
Volume | 22 |
Issue number | 1 |
State | Published - 2019 |
Bibliographical note
Funding 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).
Publisher Copyright:
© 2019, University of Waterloo. All rights reserved.
Keywords
- Bott-Taubes polytope
- Delannoy number
- F-vector
- Schröder path
- Type B associahedron
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics