Ehrhart-equivalent $\boldsymbol 3$-polytopes are equidecomposable
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- by Jakob Erbe, Christian Haase and Francisco Santos PDF
- Proc. Amer. Math. Soc. 147 (2019), 5373-5383 Request permission
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 $i$.References
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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
- MR Author ID: 661101
- ORCID: 0000-0003-4078-0913
- Email: haase@math.fu-berlin.de
- Francisco Santos
- Affiliation: Departamento de Matemáticas, Estadística y Computación, Universidad de Cantabria, 39005 Santander, Spain
- MR Author ID: 360182
- ORCID: 0000-0003-2120-9068
- Email: francisco.santos@unican.es
- 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
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 147 (2019), 5373-5383
- MSC (2010): Primary 52B10, 52B20
- DOI: https://doi.org/10.1090/proc/14626
- MathSciNet review: 4021096