# Publications

by Haase, Christian; Paffenholz, Andreas; Piechnik, Lindsay C. and Santos, Francisco

Abstract:

Unimodular triangulations of lattice polytopes and their relatives arise in algebraic geometry, commutative algebra, integer programming and, of course, combinatorics. Presumably, "most" lattice polytopes do not admit a unimodular triangulation. In this article, we survey which classes of polytopes are known to have unimodular triangulations; among them some new classes, and some not so new which have not been published elsewhere. We include a new proof of the classical result by Knudsen-Munford-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.

Reference:

Haase, Christian; Paffenholz, Andreas; Piechnik, Lindsay C. and Santos, Francisco: "Existence of unimodular triangulations - positive results", 2014.

Bibtex Entry:

@Online{1405.1687, Title = {Existence of unimodular triangulations - positive results}, Author = {Christian Haase and Andreas Paffenholz and Lindsay C. Piechnik and Francisco Santos}, Year = {2014}, Month = may, Abstract = {Unimodular triangulations of lattice polytopes and their relatives arise in algebraic geometry, commutative algebra, integer programming and, of course, combinatorics. Presumably, "most" lattice polytopes do not admit a unimodular triangulation. In this article, we survey which classes of polytopes are known to have unimodular triangulations; among them some new classes, and some not so new which have not been published elsewhere. We include a new proof of the classical result by Knudsen-Munford-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.}, Comments = {82 pages; updated since v1 did not contain the bibliography due to a LaTeX mistake}, Eprint = {1405.1687}, Eprintclass = {math.CO}, Eprinttype = {arxiv}, Oai2identifier = {1405.1687}, note = "to appear in: Memoirs of the AMS", url = "https://www.ams.org/cgi-bin/mstrack/accepted_papers/memo", Timestamp = {2014.08.21} }