Abstract
For an n-dimensional lattice simplex (Formula presented.) with vertices given by the standard basis vectors and (Formula presented.) where (Formula presented.) has positive entries, we investigate when the Ehrhart (Formula presented.) -polynomial for (Formula presented.) factors as a product of geometric series in powers of z. Our motivation is a theorem of Rodriguez-Villegas implying that when the (Formula presented.) -polynomial of a lattice polytope P has all roots on the unit circle, then the Ehrhart polynomial of P has positive coefficients. We focus on those (Formula presented.) for which (Formula presented.) has only two or three distinct entries, providing both theoretical results and conjectures/questions motivated by experimental evidence.
Original language | English |
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Pages (from-to) | 332-348 |
Number of pages | 17 |
Journal | Experimental Mathematics |
Volume | 30 |
Issue number | 3 |
DOIs | |
State | Published - 2021 |
Bibliographical note
Publisher Copyright:© 2019 Taylor & Francis Group, LLC.
Funding
The first author was partially supported by grant H98230-16-1-0045 from the U.S. National Security Agency. The second author was partially supported by a grant from the Simons Foundation #426756. This material is also based in part upon work supported by the National Science Foundation under Grant No. DMS-1440140 while both authors were in residence at the Mathematical Sciences Research Institute in Berkeley, California, during the Fall 2017 semester.
Funders | Funder number |
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National Science Foundation Arctic Social Science Program | DMS-1440140, 1440140 |
Simons Foundation | 426756 |
National Security Agency |
Keywords
- Ehrhart positivity
- h*-polynomial
- lattice simplex
- unit circle rooted
ASJC Scopus subject areas
- General Mathematics