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Existence of unimodular triangulations-positive results / Christian Haase, Andreas Paffenholz, Lindsay C. Piechnik, and Francisco Santos.
Math/Physics/Astronomy Library QA3 .A57 no.1321
Available
- Format:
- Book
- Author/Creator:
- Haase, Christian (Mathematician), author.
- Paffenholz, Andreas, author.
- Piechnik, Lindsay C., author.
- Santos, Francisco, 1968- author.
- Series:
- Memoirs of the American Mathematical Society ; no. 1321.
- Memoirs of the American Mathematical Society, 0065-9266 ; number 1321
- Language:
- English
- Subjects (All):
- Algebra, Abstract.
- Physical Description:
- v, 83 pages : illustrations ; 26 cm.
- Place of Publication:
- Providence : American Mathematical Society, [2021]
- Summary:
- 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.
- Contents:
- Methods
- Examples
- Dilations and the KMW theorem.
- Notes:
- "March 2021, volume 270, number 1321 (fifth of 7 numbers)."
- Includes bibliographical references.
- ISBN:
- 1470447169
- 9781470447168
- OCLC:
- 1243742956
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