{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T07:52:15Z","timestamp":1776844335493,"version":"3.51.2"},"reference-count":46,"publisher":"Elsevier BV","issue":"4","license":[{"start":{"date-parts":[[2004,10,1]],"date-time":"2004-10-01T00:00:00Z","timestamp":1096588800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2013,8,22]],"date-time":"2013-08-22T00:00:00Z","timestamp":1377129600000},"content-version":"vor","delay-in-days":3247,"URL":"https:\/\/www.elsevier.com\/open-access\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Symbolic Computation"],"published-print":{"date-parts":[[2004,10]]},"DOI":"10.1016\/j.jsc.2003.04.003","type":"journal-article","created":{"date-parts":[[2004,5,8]],"date-time":"2004-05-08T11:36:16Z","timestamp":1084016176000},"page":"1273-1302","source":"Crossref","is-referenced-by-count":169,"title":["Effective lattice point counting in rational convex polytopes"],"prefix":"10.1016","volume":"38","author":[{"given":"Jes\u00fas A.","family":"De Loera","sequence":"first","affiliation":[]},{"given":"Raymond","family":"Hemmecke","sequence":"additional","affiliation":[]},{"given":"Jeremiah","family":"Tauzer","sequence":"additional","affiliation":[]},{"given":"Ruriko","family":"Yoshida","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/j.jsc.2003.04.003_B1","series-title":"Integer Programming and Combinatorial Optimization (6th International IPCO Conference)","first-page":"229","article-title":"Solving a linear diophantine equations with lower and upper bounds on the variables","volume":"vol. 1412","author":"Aardal","year":"1998"},{"key":"10.1016\/j.jsc.2003.04.003_B2","series-title":"Integer Programming and Combinatorial Optimization: 9th International IPCO Conference","first-page":"350","article-title":"Hard equality constrained integer knapsacks","volume":"vol. 2337","author":"Aardal","year":"2002"},{"key":"10.1016\/j.jsc.2003.04.003_B3","series-title":"Workshop on Discrete Optimization","first-page":"5","article-title":"Non-standard approaches to integer programming","volume":"123 (1\u20133)","author":"Aardal","year":"2002"},{"key":"10.1016\/j.jsc.2003.04.003_B4","series-title":"New Directions in Combinatorial Geometry","first-page":"25","article-title":"Polyhedral cones of magic cubes and square","author":"Ahmed","year":"2003"},{"key":"10.1016\/j.jsc.2003.04.003_B5","series-title":"Proc. of 28th Annual ACM Symp. on Theory of Computing","first-page":"99","article-title":"Generating hard instance of lattice problems","author":"Ajtai","year":"1996"},{"key":"10.1016\/j.jsc.2003.04.003_B6","series-title":"Handbook of Computational Geometry","first-page":"201","author":"Aurenhammer","year":"2000"},{"key":"10.1016\/j.jsc.2003.04.003_B7","author":"Baldoni-Silva"},{"key":"10.1016\/j.jsc.2003.04.003_B8","author":"Baldoni-Silva"},{"key":"10.1016\/j.jsc.2003.04.003_B9","doi-asserted-by":"crossref","first-page":"769","DOI":"10.1287\/moor.19.4.769","article-title":"Polynomial time algorithm for counting integral points in polyhedra when the dimension is fixed","volume":"19","author":"Barvinok","year":"1994","journal-title":"Math. Oper. Res."},{"key":"10.1016\/j.jsc.2003.04.003_B10","series-title":"New Perspectives in Algebraic Combinatorics","article-title":"An algorithmic theory of lattice points in polyhedra","volume":"vol. 38","author":"Barvinok","year":"1999"},{"key":"10.1016\/j.jsc.2003.04.003_B11","first-page":"957","article-title":"Short rational generating functions for lattice point problems","volume":"16","author":"Barvinok","year":"2003","journal-title":"J. AMS"},{"issue":"3","key":"10.1016\/j.jsc.2003.04.003_B12","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1023\/A:1009853104418","article-title":"Counting lattice points by means of the residue theorem","volume":"4","author":"Beck","year":"2000","journal-title":"Ramanujan J."},{"issue":"4","key":"10.1016\/j.jsc.2003.04.003_B13","doi-asserted-by":"crossref","first-page":"623","DOI":"10.1007\/s00454-003-2850-8","article-title":"The Ehrhart polynomial of the Birkhoff polytope","volume":"30","author":"Beck","year":"2003","journal-title":"Discrete Comput. Geom."},{"key":"10.1016\/j.jsc.2003.04.003_B14","doi-asserted-by":"crossref","first-page":"653","DOI":"10.24033\/asens.1572","article-title":"Points entiers dans les poly\u00e8dres convexes","volume":"21","author":"Brion","year":"1988","journal-title":"Ann. Sci. \u00c9cole Norm. Sup."},{"key":"10.1016\/j.jsc.2003.04.003_B15","author":"Bruns"},{"key":"10.1016\/j.jsc.2003.04.003_B16","doi-asserted-by":"crossref","first-page":"206","DOI":"10.1287\/ijoc.5.2.206","article-title":"An implementation of the generalized basis reduction algorithm for integer programming","volume":"5","author":"Cook","year":"1993","journal-title":"ORSA J. Comput."},{"key":"10.1016\/j.jsc.2003.04.003_B17","series-title":"Ideals, Varieties, and Algorithms","author":"Cox","year":"1997"},{"key":"10.1016\/j.jsc.2003.04.003_B18","doi-asserted-by":"crossref","unstructured":"De Loera, J., Haws, D., Hemmecke, R., Huggins, P., Sturmfels, B., Yoshida, R., 2003. Short rational functions for toric algebra (to appear in Journal of Symbolic Computation)","DOI":"10.1016\/j.jsc.2004.02.001"},{"key":"10.1016\/j.jsc.2003.04.003_B19","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1007\/s10107-003-0383-9","article-title":"Algebraic unimodular counting","volume":"96","author":"De Loera","year":"2003","journal-title":"Math. Programming Ser. B"},{"key":"10.1016\/j.jsc.2003.04.003_B20","series-title":"Discrete Probability and Algorithms","first-page":"15","article-title":"Rectangular arrays with fixed margins","volume":"vol. 72","author":"Diaconis","year":"1995"},{"key":"10.1016\/j.jsc.2003.04.003_B21","doi-asserted-by":"crossref","first-page":"545","DOI":"10.1287\/moor.22.3.545","article-title":"On Barvinok\u2019s algorithm for counting lattice points in fixed dimension","volume":"22","author":"Dyer","year":"1997","journal-title":"Math. Oper. Res."},{"key":"10.1016\/j.jsc.2003.04.003_B22","article-title":"Polyn\u00f4mes arithm\u00e9tiques et methode des poly\u00e9dres en combinatoire","volume":"vol. 35","author":"Ehrhart","year":"1977"},{"key":"10.1016\/j.jsc.2003.04.003_B23","series-title":"Data Analysis From Statistical Foundations","first-page":"145","article-title":"Computing the exact conditional distribution for a multi-way contingency table conditional on its marginal totals","author":"Fienberg","year":"2001"},{"key":"10.1016\/j.jsc.2003.04.003_B24","author":"Fukuda"},{"key":"10.1016\/j.jsc.2003.04.003_B25","article-title":"Geometric algorithms and combinatorial optimization","volume":"vol. 2","author":"Gr\u00f6tschel","year":"1993"},{"key":"10.1016\/j.jsc.2003.04.003_B26","series-title":"Proceedings of First International Congress of Mathematical Software","article-title":"On the computation of Hilbert bases of cones","author":"Hemmecke","year":"2002"},{"key":"10.1016\/j.jsc.2003.04.003_B27","series-title":"Applied and Computational Complex Analysis","author":"Henrici","year":"1974"},{"key":"10.1016\/j.jsc.2003.04.003_B28","series-title":"Physics and Combinatorics","article-title":"Ubiquity of Kostka Polynomials","author":"Kirillov","year":"2001"},{"key":"10.1016\/j.jsc.2003.04.003_B29","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S1631-073X(02)02591-8","article-title":"La valeur optimale des programmes entiers","volume":"335","author":"Lasserre","year":"2002","journal-title":"C. R. Acad. Sci. Paris, Ser. I"},{"key":"10.1016\/j.jsc.2003.04.003_B30","doi-asserted-by":"crossref","first-page":"394","DOI":"10.1016\/S0167-6377(02)00161-X","article-title":"Solving the knapsack problem via Z-transform","volume":"30","author":"Lasserre","year":"2002","journal-title":"Oper. Res. Lett."},{"key":"10.1016\/j.jsc.2003.04.003_B31","series-title":"Discrete and Computational Geometry","first-page":"199","article-title":"Rational-function-valued valuations on polyhedra","volume":"vol. 6","author":"Lawrence","year":"1991"},{"key":"10.1016\/j.jsc.2003.04.003_B32","series-title":"Handbook of Discrete and Computational Geometry","first-page":"271","article-title":"Subdivisions and triangulations of polytopes","author":"Lee","year":"1997"},{"key":"10.1016\/j.jsc.2003.04.003_B33","doi-asserted-by":"crossref","first-page":"538","DOI":"10.1287\/moor.8.4.538","article-title":"Integer programming with a fixed number of variables","volume":"8","author":"Lenstra","year":"1983","journal-title":"Math. Oper. Res."},{"key":"10.1016\/j.jsc.2003.04.003_B34","doi-asserted-by":"crossref","first-page":"751","DOI":"10.1287\/moor.17.3.751","article-title":"The generalized basis reduction algorithm","volume":"17","author":"Lov\u00e1sz","year":"1992","journal-title":"Math. Oper. Res."},{"key":"10.1016\/j.jsc.2003.04.003_B35","volume":"vol. I\u2013II","author":"MacMahon","year":"1960"},{"key":"10.1016\/j.jsc.2003.04.003_B36","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1017\/S0963548300004193","article-title":"Fast unimodular counting","volume":"9","author":"Mount","year":"2000","journal-title":"Combin. Probab. Comput."},{"key":"10.1016\/j.jsc.2003.04.003_B37","doi-asserted-by":"crossref","first-page":"98","DOI":"10.1016\/0022-314X(72)90013-3","article-title":"Representations of integers by linear forms in nonnegative integers","volume":"4","author":"Nijehuis","year":"1972","journal-title":"J. Number Theory"},{"issue":"9","key":"10.1016\/j.jsc.2003.04.003_B38","doi-asserted-by":"crossref","first-page":"2541","DOI":"10.1090\/S0002-9939-01-05853-1","article-title":"Convex polytopes all of whose reverse lexicographic initial ideals are square-free","volume":"129","author":"Ohsugi","year":"2001","journal-title":"Proc. Amer. Math. Soc."},{"key":"10.1016\/j.jsc.2003.04.003_B39","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1006\/jcta.2001.3201","article-title":"Asymptotics of multivariate sequences, part I: smooth points of the singular variety","volume":"97","author":"Pemantle","year":"2001","journal-title":"J. Combin. Theory Ser. A."},{"key":"10.1016\/j.jsc.2003.04.003_B40","doi-asserted-by":"crossref","first-page":"2367","DOI":"10.1063\/1.526457","article-title":"The Kostant partition function for simple Lie algebras","volume":"25","author":"Schmidt","year":"1984","journal-title":"J. Math. Phys."},{"key":"10.1016\/j.jsc.2003.04.003_B41","series-title":"Theory of Linear and Integer Programming","author":"Schrijver","year":"1986"},{"key":"10.1016\/j.jsc.2003.04.003_B42","author":"Shoup"},{"key":"10.1016\/j.jsc.2003.04.003_B43","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1016\/S0167-5060(08)70717-9","article-title":"Decompositions of rational convex polytopes","volume":"6","author":"Stanley","year":"1980","journal-title":"Ann. Discrete Math."},{"key":"10.1016\/j.jsc.2003.04.003_B44","doi-asserted-by":"crossref","unstructured":"Stanley, R.P., 1997. Enumerative Combinatorics, vol. I. Cambridge","DOI":"10.1017\/CBO9780511805967"},{"key":"10.1016\/j.jsc.2003.04.003_B45","article-title":"Gr\u00f6bner bases and convex polytopes","volume":"vol. 8","author":"Sturmfels","year":"1996"},{"key":"10.1016\/j.jsc.2003.04.003_B46","author":"Szenes"}],"container-title":["Journal of Symbolic Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0747717104000422?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0747717104000422?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2020,4,2]],"date-time":"2020-04-02T03:17:21Z","timestamp":1585797441000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0747717104000422"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,10]]},"references-count":46,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2004,10]]}},"alternative-id":["S0747717104000422"],"URL":"https:\/\/doi.org\/10.1016\/j.jsc.2003.04.003","relation":{},"ISSN":["0747-7171"],"issn-type":[{"value":"0747-7171","type":"print"}],"subject":[],"published":{"date-parts":[[2004,10]]}}}