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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Ehrhart-equivalent $ \boldsymbol3$-polytopes are equidecomposable


Authors: Jakob Erbe, Christian Haase and Francisco Santos
Journal: Proc. Amer. Math. Soc. 147 (2019), 5373-5383
MSC (2010): Primary 52B10, 52B20
DOI: https://doi.org/10.1090/proc/14626
Published electronically: July 8, 2019
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Abstract: We show that if two lattice $ 3$-polytopes $ P$ and $ P'$ have the same Ehrhart function, then they are $ \operatorname {GL}_d(\mathbb{Z}) $-equidecomposable, that is, they can be partitioned into relatively open simplices $ U_1,\dots , U_k$ and $ U'_1,\dots ,U'_k$ such that $ U_i$ and $ U'_i$ are unimodularly equivalent for each $ i$.


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Additional Information

Jakob Erbe
Affiliation: Institut für Mathematik, Freie Universität Berlin, 14195 Berlin, Germany
Email: jakoberbe@gmail.com

Christian Haase
Affiliation: Institut für Mathematik, Freie Universität Berlin, 14195 Berlin, Germany
Email: haase@math.fu-berlin.de

Francisco Santos
Affiliation: Departamento de Matemáticas, Estadística y Computación, Universidad de Cantabria, 39005 Santander, Spain
Email: francisco.santos@unican.es

DOI: https://doi.org/10.1090/proc/14626
Received by editor(s): September 14, 2018
Received by editor(s) in revised form: March 1, 2019
Published electronically: July 8, 2019
Additional Notes: The second author was supported by the research training group Facets of Complexity GRK 2434 of the German Research Foundation DFG
The third author was supported by grants MTM2014-54207-P and MTM2017-83750-P of the Spanish Ministry of Science and grant EVF-2015-230 of the Einstein Foundation Berlin
Communicated by: Patricia L. Hersch
Article copyright: © Copyright 2019 American Mathematical Society