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The equivariant Ehrhart theory of the permutahedron


Authors: Federico Ardila, Mariel Supina and Andrés R. Vindas-Meléndez
Journal: Proc. Amer. Math. Soc. 148 (2020), 5091-5107
MSC (2010): Primary 14L30, 14M25, 52B15, 52B20, 05E18
DOI: https://doi.org/10.1090/proc/15113
Published electronically: September 17, 2020
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Abstract: Equivariant Ehrhart theory enumerates the lattice points in a polytope with respect to a group action. Answering a question of Stapledon, we describe the equivariant Ehrhart theory of the permutahedron, and we prove his Effectiveness Conjecture in this special case.


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Additional Information

Federico Ardila
Affiliation: Department of Mathematics, San Francisco State University, 1600 Holloway Avenue, San Francisco, California 94132; Department of Mathematics, Universidad de Los Andes, Bogota, Columbia
MR Author ID: 725066
Email: federico@sfsu.edu

Mariel Supina
Affiliation: Department of Mathematics, 970 Evans Hall, University of California, Berkeley, Berkeley, California 94720-3840
Email: mariel_supina@berkeley.edu

Andrés R. Vindas-Meléndez
Affiliation: Department of Mathematics, San Francisco State University, 1600 Holloway Avenue, San Francisco, California 94132; Department of Mathematics, 719 Patterson Office Tower, University of Kentucky, Lexington, Kentucky 40506-0027
ORCID: 0000-0002-7437-3745
Email: andres.vindas@uky.edu

DOI: https://doi.org/10.1090/proc/15113
Received by editor(s): November 22, 2019
Received by editor(s) in revised form: March 6, 2020
Published electronically: September 17, 2020
Additional Notes: This work was completed while the first author was a Spring 2019 Visiting Professor at the Simons Institute for Theoretical Computer Science in Berkeley, and a 2019–2020 Simons Fellow while on sabbatical in Bogotá.
The authors were supported by NSF Award DMS-1600609 and DMS-1855610 and Simons Fellowship 613384 (FA), the Graduate Fellowships for STEM Diversity (MS), and NSF Graduate Research Fellowship DGE-1247392 (ARVM)
Communicated by: Patricia L Hersh
Article copyright: © Copyright 2020 American Mathematical Society