@article {2019BecksmoothCS3D, AUTHOR = {Beck, Matthias and Haase, Christian and Higashitani, Akihiro and Hofscheier, Johannes and Jochemko, Katharina and Katth\"{a}n, Lukas and Micha\l ek, Mateusz}, TITLE = {Smooth centrally symmetric polytopes in dimension 3 are {IDP}}, JOURNAL = {Ann. Comb.}, FJOURNAL = {Annals of Combinatorics}, VOLUME = {23}, YEAR = {2019}, NUMBER = {2}, PAGES = {255--262}, MRCLASS = {52B20 (52B10 52B12)}, MRNUMBER = {3962856}, MRREVIEWER = {Robert\ Davis}, DOI = {10.1007/s00026-019-00418-x}, URL = {https://doi.org/10.1007/s00026-019-00418-x}, } @article{oda2008problems, title={Problems on Minkowski sums of convex lattice polytopes}, author={Oda, Tadao}, eprinttype = {arXiv}, eprint = {0812.1418}, year={2008} } @article{haase2007lattice, AUTHOR = {Haase, Christian and Nill, Benjamin and Paffenholz, Andreas and Santos, Francisco}, TITLE = {Lattice points in {M}inkowski sums}, JOURNAL = {Electron. J. Combin.}, FJOURNAL = {Electronic Journal of Combinatorics}, VOLUME = {15}, YEAR = {2008}, NUMBER = {1}, PAGES = {Note 11, 5 pp.}, DOI = {10.37236/886}, URL = {https://doi.org/10.37236/886}, } @article{caratheodory1911, title={{\"U}ber den Variabilit{\"a}tsbereich der Fourier'schen Konstanten von positiven harmonischen Funktionen}, author={Carath{\'e}odory, Constantin}, journal={Rendiconti Del Circolo Matematico di Palermo (1884-1940)}, volume={32}, number={1}, pages={193--217}, year={1911}, publisher={Springer} } @article{Bogart_2015, AUTHOR = {Bogart, Tristram and Haase, Christian and Hering, Milena and Lorenz, Benjamin and Nill, Benjamin and Paffenholz, Andreas and Rote, G\"unter and Santos, Francisco and Schenck, Hal}, TITLE = {Finitely many smooth {$d$}-polytopes with {$n$} lattice points}, JOURNAL = {Israel J. Math.}, FJOURNAL = {Israel Journal of Mathematics}, VOLUME = {207}, YEAR = {2015}, NUMBER = {1}, PAGES = {301--329}, DOI = {10.1007/s11856-015-1175-7}, URL = {https://doi.org/10.1007/s11856-015-1175-7}, } @article{Lundman_2012, title={A classification of smooth convex 3-polytopes with at most 16 lattice points}, volume={37}, DOI={10.1007/s10801-012-0363-3}, number={1}, JOURNAL = {J. Algebraic Combin.}, publisher={Springer Science and Business Media LLC}, author={Lundman, Anders}, year={2012}, pages={139-165} } @article{koelman1993generators, title={Generators for the ideal of a projectively embedded toric surface}, author={Koelman, Robert Jan}, JOURNAL = {Tohoku Math. J. (2)}, volume={45}, number={3}, pages={385--392}, year={1993}, DOI = {10.2748/tmj/1178225891}, publisher={Mathematical Institute, Tohoku University} } @book{cox2011toric, AUTHOR = {Cox, David A. and Little, John B. and Schenck, Henry K.}, TITLE = {Toric varieties}, SERIES = {Graduate Studies in Mathematics}, VOLUME = {124}, PUBLISHER = {American Mathematical Society, Providence, RI}, YEAR = {2011}, PAGES = {xxiv+841}, DOI = {10.1090/gsm/124}, URL = {https://doi.org/10.1090/gsm/124}, } @article{viet1997normal, AUTHOR = {Bruns, Winfried and Gubeladze, Joseph and Ng\^o{} Vi\^et Trung}, TITLE = {Normal polytopes, triangulations, and {K}oszul algebras}, JOURNAL = {J. Reine Angew. Math.}, FJOURNAL = {Journal f\"ur die Reine und Angewandte Mathematik. [Crelle's Journal]}, VOLUME = {485}, YEAR = {1997}, PAGES = {123--160}, DOI = {10.1515/crll.1997.485.123}, } @article{Haase_2021, AUTHOR = {Haase, Christian and Paffenholz, Andreas and Piechnik, Lindsay C. and Santos, Francisco}, TITLE = {Existence of unimodular triangulations---positive results}, JOURNAL = {Mem. Amer. Math. Soc.}, FJOURNAL = {Memoirs of the American Mathematical Society}, VOLUME = {270}, YEAR = {2021}, NUMBER = {1321}, PAGES = {v+83 pp.}, DOI = {10.1090/memo/1321}, URL = {https://doi.org/10.1090/memo/1321}, } @article{hibi2008mini, TITLE = {Mini-{W}orkshop: {P}rojective {N}ormality of {S}mooth {T}oric {V}arieties}, JOURNAL = {Oberwolfach Rep.}, FJOURNAL = {Oberwolfach Reports}, VOLUME = {4}, YEAR = {2007}, NUMBER = {3}, PAGES = {2283--2319}, ISSN = {1660-8933,1660-8941}, MRCLASS = {14-06 (14M25)}, MRNUMBER = {2432116}, } @article{gubeladze2012convex, AUTHOR = {Gubeladze, Joseph}, TITLE = {Convex normality of rational polytopes with long edges}, JOURNAL = {Adv. Math.}, FJOURNAL = {Advances in Mathematics}, VOLUME = {230}, YEAR = {2012}, NUMBER = {1}, PAGES = {372--389}, DOI = {10.1016/j.aim.2011.12.003}, URL = {https://doi.org/10.1016/j.aim.2011.12.003}, } @article{firla1999hilbert, AUTHOR = {Firla, R. T. and Ziegler, G. M.}, TITLE = {Hilbert bases, unimodular triangulations, and binary covers of rational polyhedral cones}, JOURNAL = {Discrete Comput. Geom.}, FJOURNAL = {Discrete \& Computational Geometry. An International Journal of Mathematics and Computer Science}, VOLUME = {21}, YEAR = {1999}, NUMBER = {2}, PAGES = {205--216}, DOI = {10.1007/PL00009416}, URL = {https://doi.org/10.1007/PL00009416}, } @incollection{haase2010generating, AUTHOR = {Haase, Christian and Lorenz, Benjamin and Paffenholz, Andreas}, TITLE = {Generating smooth lattice polytopes}, BOOKTITLE = {Mathematical software---{ICMS} 2010}, SERIES = {Lecture Notes in Comput. Sci.}, VOLUME = {6327}, PAGES = {315--328}, PUBLISHER = {Springer, Berlin}, YEAR = {2010}, }