Additive Number Theory and Inequalities in Ehrhart Theory
| Autor: | Alan Stapledon |
|---|---|
| Rok vydání: | 2015 |
| Předmět: |
52B20
11P21 Pure mathematics Mathematics - Number Theory Inequality General Mathematics media_common.quotation_subject 010102 general mathematics Dimension (graph theory) Lattice (group) Polytope 02 engineering and technology 01 natural sciences Connection (mathematics) FOS: Mathematics 0202 electrical engineering electronic engineering information engineering Additive number theory Mathematics - Combinatorics Mathematics::Metric Geometry 020201 artificial intelligence & image processing Combinatorics (math.CO) Number Theory (math.NT) 0101 mathematics Commutative algebra media_common Mathematics |
| Zdroj: | International Mathematics Research Notices. 2016:1497-1540 |
| ISSN: | 1687-0247 1073-7928 |
| DOI: | 10.1093/imrn/rnv186 |
| Popis: | We introduce a powerful connection between Ehrhart theory and additive number theory, and use it to produce infinitely many new classes of inequalities between the coefficients of the $h^*$-polynomial of a lattice polytope. This greatly improves upon the three known classes of inequalities, which were proved using techniques from commutative algebra and combinatorics. As an application, we deduce all possible `balanced' inequalities between the coefficients of the $h^*$-polynomial of a lattice polytope containing an interior lattice point, in dimension at most 6. 40 pages, 7 figures. Replaces `Kneser's theorem and inequalities in Ehrhart theory'. Improved dimension bounds |
| Databáze: | OpenAIRE |
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