A bijective answer to a question of simion

Richard Ehrenborg; Gábor Hetyei; Margaret Readdy

A bijective answer to a question of simion

Richard Ehrenborg, Gábor Hetyei, Margaret Readdy

Mathematics

Research output: Contribution to journal › Article › peer-review

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

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

Cite this

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AU - Hetyei, Gábor

AU - Readdy, Margaret

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PY - 2019

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N2 - 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.

AB - 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.

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KW - Delannoy number

KW - F-vector

KW - Schröder path

KW - Type B associahedron

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A bijective answer to a question of simion

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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