{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T09:25:05Z","timestamp":1775467505542,"version":"3.50.1"},"reference-count":36,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[1991,9,1]],"date-time":"1991-09-01T00:00:00Z","timestamp":683683200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Combinatorica"],"published-print":{"date-parts":[[1991,9]]},"DOI":"10.1007\/bf01205079","type":"journal-article","created":{"date-parts":[[2005,2,24]],"date-time":"2005-02-24T15:15:52Z","timestamp":1109258152000},"page":"275-293","source":"Crossref","is-referenced-by-count":31,"title":["Computing combinatorial decompositions of rings"],"prefix":"10.1007","volume":"11","author":[{"given":"Bernd","family":"Sturmfels","sequence":"first","affiliation":[]},{"given":"Neil","family":"White","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"CR1","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1016\/0001-8708(81)90028-1","volume":"39","author":"K. Baclawski","year":"1981","unstructured":"K. Baclawski: Rings with lexicographic straightening law,Advances in Math. 39 (1981), 185?213.","journal-title":"Advances in Math."},{"key":"CR2","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1016\/0001-8708(81)90027-X","volume":"39","author":"K. Baclawski","year":"1981","unstructured":"K. Baclawski, andA.M. Garsia: Combinatorial decompositions of rings,Advances in Math. 39 (1981), 155?184.","journal-title":"Advances in Math."},{"key":"CR3","unstructured":"D. Bayer: The division algorithm and the Hilbert scheme, Ph.D. Dissertation, Harvard University, 1982."},{"key":"CR4","doi-asserted-by":"crossref","unstructured":"D. Bayer, andM. Stillman: The design of MACAULAY: A system for computing in algebraic geometry and commutative algebra,Proceedings of ACM SYMSAC, 1986.","DOI":"10.1145\/32439.32471"},{"key":"CR5","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1090\/S0002-9947-1988-0965757-9","volume":"310","author":"L. J. Billera","year":"1988","unstructured":"L. J. Billera: Homology of smooth splines: Generic triangulations and a conjecture of Strang,Trans. Amer. Math. Soc. 310 (1988), 325?340.","journal-title":"Trans. Amer. Math. Soc."},{"key":"CR6","first-page":"375","volume":"91","author":"L.J. Billera","year":"1988","unstructured":"L.J. Billera, R. Cushman andJ.A. Sanders: The Stanley decomposition of the harmonic oscillator,Proc. Koninklijke Nederlandse Akademie van Wetenschappen,A 91 (1988), 375?393.","journal-title":"Proc. Koninklijke Nederlandse Akademie van Wetenschappen"},{"key":"CR7","doi-asserted-by":"crossref","first-page":"374","DOI":"10.1007\/BF01844169","volume":"4","author":"B. Buchberger","year":"1970","unstructured":"B. Buchberger: Ein algorithmisches Kriterium f\ufffdr die L\ufffdsbarkeit eines algebraischen Gleichungssystems,Aequationes Mathematicae,4 (1970), 374?383.","journal-title":"Aequationes Mathematicae"},{"key":"CR8","doi-asserted-by":"crossref","unstructured":"B. Buchberger: Gr\ufffdbner bases-an algorithmic method in polynomial ideal theory, Chapter 6 in N.K. Bose (ed.):?Multidimensional Systems Theory?, D. Reidel Publ. Comp., 1985.","DOI":"10.1007\/978-94-009-5225-6_6"},{"key":"CR9","series-title":"I.M.A. Volumes in Mathematics and its Applications","volume-title":"Scientific Software","author":"B. Buchberger","year":"1988","unstructured":"B. Buchberger: Applications of Gr\ufffdbner bases in non-linear computational geometry, in J.R. Rice (ed.):Scientific Software, I.M.A. Volumes in Mathematics and its Applications, # 14, Springer, New York, 1988."},{"key":"CR10","series-title":"I.M.A. Volumes in Mathematics and its Applications","first-page":"82","volume-title":"?Invariant Theory and Tableaux?","author":"R. Cushman","year":"1990","unstructured":"R. Cushman andJ.A. Sanders: A survey of invariant theory applied to normal forms of vectorfields with nilpotent linear part, in D. Stanton (ed.):?Invariant Theory and Tableaux?, I.M.A. Volumes in Mathematics and its Applications,19, Springer, New York, 1990, pp. 82?106."},{"key":"CR11","doi-asserted-by":"crossref","first-page":"399","DOI":"10.1016\/0167-2789(88)90028-0","volume":"30","author":"R. Cushman","year":"1988","unstructured":"R. Cushman, J.A. Sanders, N. White: Normal form for the (2;n)-nilpotent vectorfield, using invariant theory,Physica D 30 (1988), 399?412.","journal-title":"Physica D"},{"key":"CR12","unstructured":"C. De Concini, D. Eisenbud andC. Procesi: Hodge algebras, Ast\ufffdrique91 (1982)."},{"key":"CR13","volume-title":"Invariant Theory-Old and New","author":"J.A. Dieudonn\ufffd","year":"1971","unstructured":"J.A. Dieudonn\ufffd andJ.B. Carrell:Invariant Theory-Old and New, Academic Press, New York, 1971."},{"key":"CR14","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1016\/0001-8708(78)90077-4","volume":"27","author":"P. Doubilet","year":"1978","unstructured":"P. Doubilet, J.P.S. Kung, andG.C. Rota: Invariant theory, Young bitableaux, and combinatorics,Advances in Math. 27 (1978), 63?92.","journal-title":"Advances in Math."},{"key":"CR15","volume-title":"Ring Theory and Algebra","author":"D. Eisenbud","year":"1980","unstructured":"D. Eisenbud: Introduction to algebras with straightening laws, in B.R. McDonald (ed.):Ring Theory and Algebra, Proceedings of the third Oklahoma conference, Marcel Dekker, New York, 1980."},{"key":"CR16","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1016\/0001-8708(80)90006-7","volume":"38","author":"A. Garsia","year":"1980","unstructured":"A. Garsia: Combinatorial methods in the theory of Cohen-Macaulay rings,Advances in Math. 38 (1980), 299?266.","journal-title":"Advances in Math."},{"key":"CR17","first-page":"277","volume":"44","author":"T. Hibi","year":"1986","unstructured":"T. Hibi: Every affine graded ring has a Hodge algebra structure,Rend. Sem. Mat. Univer. Politecn. Torino 44 (1986), 277?286.","journal-title":"Rend. Sem. Mat. Univer. Politecn. Torino"},{"key":"CR18","doi-asserted-by":"crossref","first-page":"473","DOI":"10.1007\/BF01208503","volume":"36","author":"D. Hilbert","year":"1890","unstructured":"D. Hilbert: \ufffdber die Theorie der algebraischen Formen,Math. Annalen 36 (1890), 473?534.","journal-title":"Math. Annalen"},{"key":"CR19","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1016\/0001-8708(74)90067-X","volume":"13","author":"M. Hochster","year":"1974","unstructured":"M. Hochster andJ. Roberts: Rings of invariants of reductive groups acting on regular rings are Cohen-Macaulay,Advances in Math. 13 (1974), 115?175.","journal-title":"Advances in Math."},{"key":"CR20","doi-asserted-by":"crossref","first-page":"1020","DOI":"10.2307\/2373744","volume":"93","author":"M. Hochster","year":"1971","unstructured":"M. Hochster andJ.A. Eagon: Cohen-Macaulay rings, invariant theory, and the generic perfection of determinanatal loci,American J. Math. 93 (1971), 1020?1058.","journal-title":"American J. Math."},{"key":"CR21","doi-asserted-by":"crossref","first-page":"118","DOI":"10.1016\/0001-8708(79)90038-0","volume":"32","author":"W.C. Huffman","year":"1979","unstructured":"W.C. Huffman andN.J.A. Sloane: Most primitive groups have messy invariants,Advances in Mathematics 32 (1979), 118?127.","journal-title":"Advances in Mathematics"},{"key":"CR22","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1307\/mmj\/1029002160","volume":"26","author":"G. Kempf","year":"1979","unstructured":"G. Kempf: The Hochster-Roberts theorem of invariant theory,Michigan Math. J. 26 (1979), 19?32.","journal-title":"Michigan Math. J."},{"key":"CR23","doi-asserted-by":"crossref","unstructured":"G. Kempf: Computing invariants, in S.S. Koh (ed.):Invariant Theory, Springer Lecture Notes # 1278, Heidelberg, 1987.","DOI":"10.1007\/BFb0078808"},{"key":"CR24","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1007\/BF01215121","volume":"167","author":"B. Kind","year":"1979","unstructured":"B. Kind andP. Kleinschmidt: Sch\ufffdlbare Cohen-Macaulay-Komplexe und ihre Parametrisierung,Math. Zeitschrift 167 (1979), 173?179.","journal-title":"Math. Zeitschrift"},{"key":"CR25","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1090\/S0273-0979-1984-15188-7","volume":"10","author":"J.P.S. Kung","year":"1984","unstructured":"J.P.S. Kung andG.-C. Rota: The invariant theory of binary forms,Bull. American Math. Soc. 10 (1984), 27?85.","journal-title":"Bull. American Math. Soc."},{"key":"CR26","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1007\/BF01456821","volume":"77","author":"E. Noether","year":"1916","unstructured":"E. Noether: Der Endlichkeitssatz der Invarianten endlicher Gruppen,Math. Annalen 77 (1916), 89?92.","journal-title":"Math. Annalen"},{"key":"CR27","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1017\/S0305004100030917","volume":"52","author":"D. Rees","year":"1956","unstructured":"D. Rees: A basis theorem for polynomial rings,Cambridge Phil. Soc. Proc. 52 (1956), 12?16.","journal-title":"Cambridge Phil. Soc. Proc."},{"key":"CR28","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1016\/S0747-7171(88)80047-6","volume":"6","author":"D. Shannon","year":"1988","unstructured":"D. Shannon andM. Sweedler: Using Gr\ufffdbner bases to determine subalgebra membership, split surjective algebra homomorphisms, and birational equivalence,J. Symbolic Computation 6 (1988), 267?273.","journal-title":"J. Symbolic Computation"},{"key":"CR29","doi-asserted-by":"crossref","first-page":"82","DOI":"10.1080\/00029890.1977.11994294","volume":"84","author":"N.J.A. Sloane","year":"1977","unstructured":"N.J.A. Sloane: Error-correcting codes and invariant theory: New applications of a nineteenth-century technique,American Math. Monthly 84 (1977), 82?107.","journal-title":"American Math. Monthly"},{"key":"CR30","doi-asserted-by":"crossref","first-page":"475","DOI":"10.1090\/S0273-0979-1979-14597-X","volume":"1","author":"R.P. Stanley","year":"1979","unstructured":"R.P. Stanley: Invariants of finite groups and their applications to combinatorics,Bulletin Amer. Math. Soc. 1 (1979), 475?511.","journal-title":"Bulletin Amer. Math. Soc."},{"key":"CR31","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1007\/BF01394054","volume":"68","author":"R.P. Stanley","year":"1982","unstructured":"R.P. Stanley: Linear diophantine equations and local cohomology,Inventiones math. 68 (1982) 175?193.","journal-title":"Inventiones math."},{"key":"CR32","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1016\/0001-8708(78)90045-2","volume":"28","author":"R.P. Stanley","year":"1978","unstructured":"R.P. Stanley: Hilbert functions of graded algebras,Advances in Math. 28 (1978), 57?83.","journal-title":"Advances in Math."},{"key":"CR33","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4899-6752-7","volume-title":"Combinatorics and Commutative Algebra","author":"R. P. Stanley","year":"1983","unstructured":"R. P. Stanley:Combinatorics and Commutative Algebra, Birkh\ufffduser, Boston, 1983."},{"key":"CR34","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1007\/BF03322623","volume":"15","author":"B. Sturmfels","year":"1989","unstructured":"B. Sturmfels: Computing final polynomials and final syzygies using Buchberger's Gr\ufffdbner bases method,Resultate der Mathematik,15 (1989), 351?360.","journal-title":"Resultate der Mathematik"},{"key":"CR35","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1016\/0001-8708(89)90053-4","volume":"76","author":"B. Sturmfels","year":"1989","unstructured":"B. Sturmfels andN. White: Gr\ufffdbner bases and invariant theory,Advances in Math.,76 (1989), 245?259.","journal-title":"Advances in Math."},{"key":"CR36","doi-asserted-by":"crossref","first-page":"481","DOI":"10.1137\/0604049","volume":"4","author":"W. Whiteley","year":"1983","unstructured":"W. Whiteley andN. White: The algebraic geometry of stresses in frameworks,SIAM J. Alg. Discr. Meth. 4 (1983), 481?511.","journal-title":"SIAM J. Alg. Discr. Meth."}],"container-title":["Combinatorica"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF01205079.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/BF01205079\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF01205079","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,4,5]],"date-time":"2020-04-05T22:43:49Z","timestamp":1586126629000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BF01205079"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1991,9]]},"references-count":36,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1991,9]]}},"alternative-id":["BF01205079"],"URL":"https:\/\/doi.org\/10.1007\/bf01205079","relation":{},"ISSN":["0209-9683","1439-6912"],"issn-type":[{"value":"0209-9683","type":"print"},{"value":"1439-6912","type":"electronic"}],"subject":[],"published":{"date-parts":[[1991,9]]}}}