A bijective answer to a question of simion

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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 languageEnglish
Article number19.1.2
JournalJournal of Integer Sequences
Issue number1
StatePublished - 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.


  • Bott-Taubes polytope
  • Delannoy number
  • F-vector
  • Schröder path
  • Type B associahedron

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics


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