Publications

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