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Thin Polytopes: Lattice Polytopes With Vanishing Local h*-Polynomial.
- Source :
-
IMRN: International Mathematics Research Notices . Apr2024, Vol. 2024 Issue 7, p5619-5657. 39p. - Publication Year :
- 2024
-
Abstract
- In this paper, we study the novel notion of thin polytopes: lattice polytopes whose local |$h^{*}$| -polynomials vanish. The local |$h^{*}$| -polynomial is an important invariant in modern Ehrhart theory. Its definition goes back to Stanley with fundamental results achieved by Karu, Borisov, and Mavlyutov; Schepers; and Katz and Stapledon. The study of thin simplices was originally proposed by Gelfand, Kapranov, and Zelevinsky, where in this case the local |$h^{*}$| -polynomial simply equals its so-called box polynomial. Our main results are the complete classification of thin polytopes up to dimension 3 and the characterization of thinness for Gorenstein polytopes. The paper also includes an introduction to the local |$h^{*}$| -polynomial with a survey of previous results. [ABSTRACT FROM AUTHOR]
- Subjects :
- *LEANNESS
*POLYNOMIALS
*POLYTOPES
*CLASSIFICATION
*DEFINITIONS
Subjects
Details
- Language :
- English
- ISSN :
- 10737928
- Volume :
- 2024
- Issue :
- 7
- Database :
- Academic Search Index
- Journal :
- IMRN: International Mathematics Research Notices
- Publication Type :
- Academic Journal
- Accession number :
- 176726311
- Full Text :
- https://doi.org/10.1093/imrn/rnad231