{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,26]],"date-time":"2025-11-26T16:14:08Z","timestamp":1764173648307},"reference-count":16,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2010,6,12]],"date-time":"2010-06-12T00:00:00Z","timestamp":1276300800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Comput Geom"],"published-print":{"date-parts":[[2011,4]]},"DOI":"10.1007\/s00454-010-9271-2","type":"journal-article","created":{"date-parts":[[2010,6,11]],"date-time":"2010-06-11T15:39:34Z","timestamp":1276270774000},"page":"449-461","source":"Crossref","is-referenced-by-count":3,"title":["Smooth Fano Polytopes Arising from Finite Partially Ordered Sets"],"prefix":"10.1007","volume":"45","author":[{"given":"Takayuki","family":"Hibi","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Akihiro","family":"Higashitani","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2010,6,12]]},"reference":[{"key":"9271_CR1","first-page":"493","volume":"3","author":"V.V. Batyrev","year":"1994","unstructured":"Batyrev, V.V.: Dual polyhedra and mirror symmetry for Calabi-Yau hypersurfaces in toric varieties. J.\u00a0Algeb. Geom. 3, 493\u2013535 (1994)","journal-title":"J.\u00a0Algeb. Geom."},{"key":"9271_CR2","doi-asserted-by":"crossref","first-page":"121","DOI":"10.5802\/aif.2175","volume":"56","author":"C. Casagrande","year":"2006","unstructured":"Casagrande, C.: The number of vertices of a Fano polytope. Ann. Inst. Fourier 56, 121\u2013130 (2006)","journal-title":"Ann. Inst. Fourier"},{"key":"9271_CR3","doi-asserted-by":"crossref","first-page":"93","DOI":"10.2969\/aspm\/01110093","volume":"110","author":"T. Hibi","year":"1987","unstructured":"Hibi, T.: Distributive lattices, affine semigroup rings and algebras with straightening laws. Adv. Stud. Pure Math. 110, 93\u2013109 (1987)","journal-title":"Adv. Stud. Pure Math."},{"issue":"2","key":"9271_CR4","doi-asserted-by":"crossref","first-page":"101","DOI":"10.2748\/tmj\/1145390208","volume":"58","author":"A.M. Kasprzyk","year":"2006","unstructured":"Kasprzyk, A.M.: Toric Fano threefolds with terminal singularities. Tohoku Mat. J. 58(2), 101\u2013121 (2006)","journal-title":"Tohoku Mat. J."},{"key":"9271_CR5","unstructured":"Kasprzyk, A.M.: Canonical toric Fano threefolds. arXiv:0806.2604v2 [math.AG]"},{"key":"9271_CR6","doi-asserted-by":"crossref","first-page":"853","DOI":"10.4310\/ATMP.1998.v2.n4.a5","volume":"2","author":"M. Kreuzer","year":"1998","unstructured":"Kreuzer, M., Skarke, H.: Classification of polyhedra in three dimensions. Adv. Theor. Math. Phys. 2, 853\u2013871 (1998)","journal-title":"Adv. Theor. Math. Phys."},{"key":"9271_CR7","doi-asserted-by":"crossref","first-page":"1209","DOI":"10.4310\/ATMP.2000.v4.n6.a2","volume":"4","author":"M. Kreuzer","year":"2000","unstructured":"Kreuzer, M., Skarke, H.: Complete classification of reflexive polyhedra in four dimensions. Adv. Theor. Math. Phys. 4, 1209\u20131230 (2000)","journal-title":"Adv. Theor. Math. Phys."},{"key":"9271_CR8","doi-asserted-by":"crossref","first-page":"453","DOI":"10.1007\/s00454-006-1294-3","volume":"38","author":"T. Lam","year":"2007","unstructured":"Lam, T., Postnikov, A.: Alcoved polytopes. I. Discrete Comput. Geom. 38, 453\u2013478 (2007)","journal-title":"Discrete Comput. Geom."},{"key":"9271_CR9","unstructured":"Nill, B., \u00d8bro, M.: \u211a-factorial Gorenstein toric Fano varieties with large Picard number. arXiv:0805.4533v1 [math.AG]"},{"key":"9271_CR10","unstructured":"\u00d8bro, M.: An algorithm for the classification of smooth Fano polytopes. arXiv:0704.0049v1 [math.CO]"},{"key":"9271_CR11","doi-asserted-by":"crossref","first-page":"131","DOI":"10.2969\/aspm\/00110131","volume":"1","author":"M. Reid","year":"1983","unstructured":"Reid, M.: Minimal models of canonical 3-folds. Adv. Stud. Pure Math., Algeb. Var. Anal. Var. 1, 131\u2013180 (1983)","journal-title":"Adv. Stud. Pure Math., Algeb. Var. Anal. Var."},{"key":"9271_CR12","volume-title":"Theory of Linear and Integer Programming","author":"A. Schrijver","year":"1986","unstructured":"Schrijver, A.: Theory of Linear and Integer Programming. Wiley, New York (1986)"},{"key":"9271_CR13","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4615-9763-6","volume-title":"Enumerative Combinatorics","author":"R.P. Stanley","year":"1986","unstructured":"Stanley, R.P.: Enumerative Combinatorics, vol.\u00a01. Wadsworth & Brooks\/Cole, Monterey (1986)"},{"key":"9271_CR14","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1007\/BF02187680","volume":"1","author":"R.P. Stanley","year":"1986","unstructured":"Stanley, R.P.: Two poset polytopes. Discrete Comput. Geom. 1, 9\u201323 (1986)","journal-title":"Discrete Comput. Geom."},{"key":"9271_CR15","doi-asserted-by":"crossref","first-page":"809","DOI":"10.1016\/S0195-6698(03)00091-X","volume":"24","author":"H. Thomas","year":"2003","unstructured":"Thomas, H.: Order-preserving maps from a poset to a chain, the order polytope, and the Todd class of the associated toric variety. Eur J. Combin. 24, 809\u2013814 (2003)","journal-title":"Eur J. Combin."},{"key":"9271_CR16","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1023\/A:1022469218716","volume":"5","author":"D.G. Wagner","year":"1996","unstructured":"Wagner, D.G.: Singularities of toric varieties associated with finite distributive lattices. J. Algeb. Comb. 5, 149\u2013165 (1996)","journal-title":"J. Algeb. Comb."}],"container-title":["Discrete & Computational Geometry"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-010-9271-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00454-010-9271-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-010-9271-2","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,30]],"date-time":"2019-05-30T02:02:16Z","timestamp":1559181736000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00454-010-9271-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,6,12]]},"references-count":16,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2011,4]]}},"alternative-id":["9271"],"URL":"https:\/\/doi.org\/10.1007\/s00454-010-9271-2","relation":{},"ISSN":["0179-5376","1432-0444"],"issn-type":[{"value":"0179-5376","type":"print"},{"value":"1432-0444","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,6,12]]}}}