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Existence of unimodular triangulations-positive results
Unimodular triangulations of lattice polytopes arise in algebraic geometry, commutative algebra, integer programming and, of course, combinatorics. In this article, we review several classes of polytopes that do have unimodular triangulations and constructions that preserve their existence. We inclu...
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| Auteurs principaux : | , , , |
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| Format : | Livre |
| Langue : | anglais |
| Titre complet : | Existence of unimodular triangulations-positive results / Christian Haase, Andreas Paffenholz, Lindsay C. Piechnik, Francisco Santos |
| Publié : |
Providence, RI :
American Mathematical Society
, C 2021 |
| Description matérielle : | 1 vol. (v-83 p.) |
| Collection : | Memoirs of the American Mathematical Society ; 1321 |
| Sujets : |
| Résumé : | Unimodular triangulations of lattice polytopes arise in algebraic geometry, commutative algebra, integer programming and, of course, combinatorics. In this article, we review several classes of polytopes that do have unimodular triangulations and constructions that preserve their existence. We include, in particular, the first effective proof of the classical result by Knudsen-Mumford-Waterman stating that every lattice polytope has a dilation that admits a unimodular triangulation. Our proof yields an explicit (although doubly exponential) bound for the dilation factor |
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| Notes : | March 2021, volume 270, number 1321 (fifth of 7 numbers). |
| Bibliographie : | Bibliogr. p. 77-83 |
| ISBN : | 978-1-4704-4716-8 1-4704-4716-9 |