{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,26]],"date-time":"2025-11-26T04:28:08Z","timestamp":1764131288291},"publisher-location":"Berlin, Heidelberg","reference-count":25,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783540427759"},{"type":"electronic","value":"9783540455066"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2001]]},"DOI":"10.1007\/3-540-45506-x_9","type":"book-chapter","created":{"date-parts":[[2007,8,28]],"date-time":"2007-08-28T10:36:53Z","timestamp":1188297413000},"page":"119-135","source":"Crossref","is-referenced-by-count":11,"title":["Division-Free Algorithms for the Determinant and the Pfaffian: Algebraic and Combinatorial Approaches"],"prefix":"10.1007","author":[{"given":"G\u00fcnter","family":"Rote","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2001,10,23]]},"reference":[{"key":"9_CR1","unstructured":"Martin Aigner, Lattice paths and determinants. In: Computational Discrete Mathematics, ed. Helmut Alt, (this volume), Lecture Notes Comput. Sci., Vol. 2122 2001, pp. 1\u201312."},{"key":"9_CR2","doi-asserted-by":"publisher","first-page":"565","DOI":"10.2307\/2004533","volume":"22","author":"E. H. Bareiss","year":"1968","unstructured":"Erwin H. Bareiss, Sylvester\u2019s identity and multistep integer-preserving Gaussian elimination. Math. Comput. 22 (1968), 565\u2013578.","journal-title":"Math. Comput."},{"key":"9_CR3","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1016\/0020-0190(84)90018-8","volume":"18","author":"S. J. Berkowitz","year":"1984","unstructured":"Stuart J. Berkowitz, On computing the determinant in small parallel time using a small number of processors. Inf. Process. Lett. 18 (1984), 147\u2013150.","journal-title":"Inf. Process. Lett."},{"key":"9_CR4","doi-asserted-by":"publisher","first-page":"241","DOI":"10.1016\/S0019-9958(82)90766-5","volume":"52","author":"A. Borodin","year":"1982","unstructured":"Allan Borodin, Joachim von zur Gathen, John Hopcroft, Fast parallel matrix and GCD computations. Inf. Control 52 (1982), 241\u2013256","journal-title":"Inf. Control"},{"key":"9_CR5","volume-title":"Solution num\u00e9rique des \u00e9quations alg\u00e9briques, tome II: syst\u00e9mes des plusieurs \u00e9quations","author":"E. Durant","year":"1961","unstructured":"E. Durant, Solution num\u00e9rique des \u00e9quations alg\u00e9briques, tome II: syst\u00e9mes des plusieurs \u00e9quations. Masson & Cie., Paris 1961."},{"key":"9_CR6","doi-asserted-by":"crossref","first-page":"241","DOI":"10.6028\/jres.071B.033","volume":"71","author":"J. Edmonds","year":"1967","unstructured":"Jack Edmonds, Systems of distinct representatives and linear algebra. J. Res. Nat. Bur. Standards, Sect. B 71 (1967), 241\u2013245.","journal-title":"J. Res. Nat. Bur. Standards, Sect. B"},{"key":"9_CR7","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1051\/ro\/1997310202031","volume":"31","author":"J. Edmonds","year":"1997","unstructured":"Jack Edmonds, J.-F. Maurras, Note sur les Q-matrices d\u2019Edmonds. RAIRO, Rech. op\u00e9r. 31 (1997), 203\u2013209.","journal-title":"RAIRO, Rech. op\u00e9r."},{"key":"9_CR8","unstructured":"D. K. Faddeyev, V. N. Faddeyeva, Vy\u010dislitel\u0144ye metody lineynoy algebry (in Russian), Moscow, 1960. English translation: D. K. Faddeev, V. N. Faddeeva, Numerical Methods of Linear Algebra. Freeman, San Francisco 1963. German translation: D. K. Faddejew, W. N. Faddejewa, Numerische Methoden der linearen Algebra, several editions since 1964."},{"key":"9_CR9","doi-asserted-by":"publisher","first-page":"269","DOI":"10.1016\/0166-218X(92)00034-J","volume":"51","author":"G. Galbiati","year":"1994","unstructured":"G. Galbiati and Franceso Maffioli, On the computation of pfaffians. Discr. Appl. Math. 51 (1994), 269\u2013275.","journal-title":"Discr. Appl. Math"},{"key":"9_CR10","unstructured":"Donald E. Knuth, Overlapping Pfaffians. Electron. J. Comb. 3 (1996), No. 2, article R5, 13 pp. Printed version: J. Comb. 3 (1996), No. 2, 147-159."},{"key":"9_CR11","first-page":"67","volume":"B42q","author":"C. Krattenthaler","year":"1999","unstructured":"Christian Krattenthaler, Advanced determinant calculus. S\u00e9minaire Lotharingien de Combinatoire B42q (1999), 67 pp.","journal-title":"S\u00e9minaire Lotharingien de Combinatoire"},{"key":"9_CR12","unstructured":"L\u00e1szl\u00f3 Lov\u00e1sz, M. D. Plummer, Matching Theory. Ann. Discr. Math., Vol. 29. North-Holland Mathematics Studies, Vol. 121. Amsterdam 1986."},{"key":"9_CR13","unstructured":"Meena Bhaskar Mahajan, P R Subramanya, V Vinay, A combinatorial algorithm for Pfaffians. In: Computing and combinatorics. Proc. 5th annual international conference. (COCOON\u2019 99), Tokyo, July 1999, ed. Takao Asano et al., Lecture Notes Comput. Sci. 1627, Springer-Verlag, pp. 134\u2013143(1999). Extended version: DIMACS Technical Report 99-39, Rutgers University, July 1999."},{"key":"9_CR14","unstructured":"Meena Bhaskar Mahajan, V Vinay, Determinant: Combinatorics, algorithms, and complexity. Chicago J. Theor. Comput. Sci., Vol. 1997, Article no. 1997-5, 26 pp."},{"key":"9_CR15","doi-asserted-by":"publisher","first-page":"474","DOI":"10.1137\/S0895480198338827","volume":"12","author":"M. Mahajan","year":"1999","unstructured":"Meena Mahajan, V. Vinay, Determinant: Old algorithms, new insights. SIAM J. Discrete Math. 12 (1999), 474\u2013490.","journal-title":"SIAM J. Discrete Math"},{"key":"9_CR16","volume-title":"A Treatise on the Theory of Determinants","author":"T. Muir","year":"1882","unstructured":"Thomas Muir, A Treatise on the Theory of Determinants. MacMillan and Co., London 1882; repr. Dover, New York 1960."},{"key":"9_CR17","series-title":"Computing Suppl.","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1007\/978-3-7091-9076-0_9","volume-title":"Computational graph theory","author":"G. Rote","year":"1990","unstructured":"G\u00fcnter Rote, Path problems in graphs. In: Computational graph theory, ed. Gottfried Tinhofer et al., Computing Suppl. 7, 155\u2013189, Springer-Verlag, Wien1990."},{"issue":"1961\u201364","key":"9_CR18","first-page":"211","volume":"66","author":"D. E. Rutherford","year":"1964","unstructured":"D. E. Rutherford, The Cayley-Hamilton theorem for semi-rings. Proc. Roy. Soc. Edinburgh, Sect. A 66(1961\u201364), 211\u2013215(1964).","journal-title":"Proc. Roy. Soc. Edinburgh"},{"key":"9_CR19","doi-asserted-by":"publisher","first-page":"424","DOI":"10.1214\/aoms\/1177731540","volume":"13","author":"P. A. Samuelson","year":"1942","unstructured":"Paul A. Samuelson, A method of determining explicitly the coefficients of the characteristic equation. Ann. Math. Statist. 13 (1942), 424\u2013429.","journal-title":"Ann. Math. Statist."},{"key":"9_CR20","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-4968-9","volume-title":"Constructive combinatorics","author":"D. Stanton","year":"1986","unstructured":"Dennis Stanton, Dennis White, Constructive combinatorics. Springer-Verlag, New York 1986."},{"key":"9_CR21","doi-asserted-by":"publisher","first-page":"96","DOI":"10.1016\/0001-8708(90)90070-4","volume":"83","author":"J. R. Stembridge","year":"1990","unstructured":"John R. Stembridge, Nonintersecting paths, pfaffians, and plane partitions. Adv. Math. 83 (1990), 96\u2013113.","journal-title":"Adv. Math"},{"key":"9_CR22","first-page":"184","volume":"264","author":"V. Strassen","year":"1973","unstructured":"Volker Strassen, Vermeidung von Divisionen. J. reine angew. Math. 264 (1973), 184\u2013202.","journal-title":"J. reine angew. Math"},{"key":"9_CR23","doi-asserted-by":"publisher","first-page":"273","DOI":"10.1016\/0012-365X(83)90164-4","volume":"43","author":"H. Straubing","year":"1983","unstructured":"Howard Straubing, A combinatorial proof of the Cayley-Hamilton theorem. Discrete Math. 43 (1983), 273\u2013279.","journal-title":"Discrete Math"},{"key":"9_CR24","doi-asserted-by":"crossref","unstructured":"Leslie G. Valiant, Why is Boolean complexity theory difficult? In: Boolean Function Complexity, ed. M. S. Paterson, LMS Lecture Notes Series, Vol. 169, Cambridge Univ. Press, 1992, pp. 84\u201394.","DOI":"10.1017\/CBO9780511526633.008"},{"key":"9_CR25","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1016\/0012-365X(85)90192-X","volume":"56","author":"D. Zeilberger","year":"1985","unstructured":"Doron Zeilberger, A combinatorial approach to matrix algebra. Discrete Math. 56 (1985), 61\u201372.","journal-title":"Discrete Math"}],"container-title":["Lecture Notes in Computer Science","Computational Discrete Mathematics"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/3-540-45506-X_9","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,2]],"date-time":"2019-05-02T13:09:21Z","timestamp":1556802561000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/3-540-45506-X_9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001]]},"ISBN":["9783540427759","9783540455066"],"references-count":25,"URL":"https:\/\/doi.org\/10.1007\/3-540-45506-x_9","relation":{},"ISSN":["0302-9743"],"issn-type":[{"type":"print","value":"0302-9743"}],"subject":[],"published":{"date-parts":[[2001]]}}}