{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,10]],"date-time":"2025-11-10T11:44:25Z","timestamp":1762775065275,"version":"build-2065373602"},"publisher-location":"New York, NY, USA","reference-count":27,"publisher":"ACM","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12471477, 11971050"],"award-info":[{"award-number":["12471477, 11971050"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2025,7,28]]},"DOI":"10.1145\/3747199.3747558","type":"proceedings-article","created":{"date-parts":[[2025,11,10]],"date-time":"2025-11-10T10:51:17Z","timestamp":1762771877000},"page":"160-168","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["On the Degrees of Reduced Gr\u00f6bner Bases of Products of Determinantal Ideals"],"prefix":"10.1145","author":[{"ORCID":"https:\/\/orcid.org\/0009-0009-3353-3034","authenticated-orcid":false,"given":"Qiuye","family":"Song","sequence":"first","affiliation":[{"name":"LMIB-School of Mathematical Sciences, Beihang University, Beijing, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5070-5928","authenticated-orcid":false,"given":"Chenqi","family":"Mou","sequence":"additional","affiliation":[{"name":"LMIB-School of Mathematical Sciences, Beihang University, Beijing, China and Sino-French Laboratory for Mathematics, Hangzhou International Innovation Institute of Beihang University, Hangzhou, China"}]}],"member":"320","published-online":{"date-parts":[[2025,11,10]]},"reference":[{"key":"e_1_3_3_1_2_2","doi-asserted-by":"crossref","unstructured":"David Bernstein and Andrei Zelevinsky. 1993. Combinatorics of maximal minors. Journal of Algebraic Combinatorics 2 (1993) 111\u2013121.","DOI":"10.1023\/A:1022492222930"},{"key":"e_1_3_3_1_3_2","doi-asserted-by":"crossref","unstructured":"Winfried Bruns and Aldo Conca. 1998. KRS and powers of determinantal ideals. Compositio Mathematica 111 1 (1998) 111\u2013122.","DOI":"10.1023\/A:1000287107308"},{"key":"e_1_3_3_1_4_2","doi-asserted-by":"crossref","unstructured":"Winfried Bruns and Aldo Conca. 2001. Algebras of minors. Journal of Algebra 246 1 (2001) 311\u2013330.","DOI":"10.1006\/jabr.2001.8964"},{"key":"e_1_3_3_1_5_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-007-1092-4_2"},{"key":"e_1_3_3_1_6_2","doi-asserted-by":"crossref","unstructured":"Winfried Bruns and Micha\u0142 Kwieci\u0144ski. 2000. Generic graph construction ideals and Greene\u2019s theorem. Mathematische Zeitschrift 233 (2000) 115\u2013126.","DOI":"10.1007\/PL00004784"},{"key":"e_1_3_3_1_7_2","volume-title":"Determinantal Rings","author":"Bruns Winfried","year":"2006","unstructured":"Winfried Bruns and Udo Vetter. 2006. Determinantal Rings. Springer."},{"key":"e_1_3_3_1_8_2","unstructured":"B. Buchberger. 1965. Ein Algorithmus zum Auffinden der Basiselemente des Restklassenrings nach einem nulldimensionalen Polynomideal. Ph.\u00a0D. Dissertation. Universit\u00e4t Innsbruck Austria."},{"key":"e_1_3_3_1_9_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-009-5225-6_6"},{"key":"e_1_3_3_1_10_2","doi-asserted-by":"crossref","unstructured":"Leandro Caniglia Jorge\u00a0A Guccione and Juan\u00a0J Guccione. 1990. Ideals of generic minors. Communications in Algebra 18 8 (1990) 2633\u20132640.","DOI":"10.1080\/00927879008824043"},{"key":"e_1_3_3_1_11_2","doi-asserted-by":"crossref","unstructured":"Aldo Conca. 1997. Gr\u00f6bner bases of powers of ideals of maximal minors. Journal of Pure and Applied Algebra 121 3 (1997) 223\u2013231.","DOI":"10.1016\/S0022-4049(96)00061-8"},{"key":"e_1_3_3_1_12_2","volume-title":"Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra","author":"Cox David","year":"1997","unstructured":"David Cox, John Little, and Donal O\u2019Shea. 1997. Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra. Springer, New York."},{"key":"e_1_3_3_1_13_2","doi-asserted-by":"crossref","unstructured":"Corrado DeConcini David Eisenbud Claudio Procesi et\u00a0al. 1980. Young diagrams and determinantal varieties. Inventiones Mathematicae 56 1 (1980) 129\u2013165.","DOI":"10.1007\/BF01392548"},{"key":"e_1_3_3_1_14_2","doi-asserted-by":"crossref","unstructured":"Peter Doubilet Gian-Carlo Rota and Joel Stein. 1974. On the foundations of combinatorial theory. IX. Combinatorial methods in invariant theory. Studies in Appl. Math 53 3 (1974) 185\u2013216.","DOI":"10.1002\/sapm1974533185"},{"key":"e_1_3_3_1_15_2","doi-asserted-by":"crossref","unstructured":"Jean-Charles Faug\u00e8re. 1999. A new efficient algorithm for computing Gr\u00f6bner bases (F4). Journal of Pure and Applied Algebra 139 1\u20133 (1999) 61\u201388.","DOI":"10.1016\/S0022-4049(99)00005-5"},{"key":"e_1_3_3_1_16_2","first-page":"75","volume-title":"Proceedings of ISSAC 2002","author":"Faug\u00e8re Jean-Charles","year":"2002","unstructured":"Jean-Charles Faug\u00e8re. 2002. A new efficient algorithm for computing Gr\u00f6bner bases without reduction to zero (F5). In Proceedings of ISSAC 2002, Teo Mora (Ed.). ACM Press, 75\u201383."},{"key":"e_1_3_3_1_17_2","volume-title":"Young Tableaux: With Applications to Representation Theory and Geometry","author":"Fulton William","year":"1997","unstructured":"William Fulton. 1997. Young Tableaux: With Applications to Representation Theory and Geometry. Number\u00a035. Cambridge University Press."},{"key":"e_1_3_3_1_18_2","doi-asserted-by":"publisher","DOI":"10.1145\/3597066.3597077"},{"key":"e_1_3_3_1_19_2","first-page":"400","volume-title":"Proceedings of ISSAC 2024","author":"Gopalakrishnan Sriram","year":"2024","unstructured":"Sriram Gopalakrishnan, Vincent Neiger, and Mohab Safey El\u00a0Din. 2024. Optimized Gr\u00f6bner basis algorithms for maximal determinantal ideals and critical point computations. In Proceedings of ISSAC 2024. 400\u2013409."},{"key":"e_1_3_3_1_20_2","doi-asserted-by":"crossref","unstructured":"Curtis Greene. 1974. An extension of Schensted\u2019s theorem. Advances in Mathematics 14 2 (1974) 254\u2013265.","DOI":"10.1016\/0001-8708(74)90031-0"},{"key":"e_1_3_3_1_21_2","doi-asserted-by":"crossref","unstructured":"J\u00fcrgen Herzog and Ng\u00f4\u00a0Vi\u00eat Trung. 1992. Gr\u00f6bner bases and multiplicity of determinantal and Pfaffian ideals. Advances in Mathematics 96 1 (1992) 1\u201337.","DOI":"10.1016\/0001-8708(92)90050-U"},{"key":"e_1_3_3_1_22_2","doi-asserted-by":"crossref","unstructured":"Donald Knuth. 1970. Permutations matrices and generalized Young tableaux. Pacific J. Math. 34 3 (1970) 709\u2013727.","DOI":"10.2140\/pjm.1970.34.709"},{"key":"e_1_3_3_1_23_2","doi-asserted-by":"crossref","unstructured":"Yonghao Ma. 1994. On the minors defined by a generic matrix. Journal of Symbolic Computation 18 6 (1994) 503\u2013518.","DOI":"10.1006\/jsco.1994.1062"},{"key":"e_1_3_3_1_24_2","first-page":"354","volume-title":"International Congress on Mathematical Software","author":"Mou Chenqi","year":"2024","unstructured":"Chenqi Mou, Qiuye Song, and Yutong Zhou. 2024. DetGB: A software package for computing Gr\u00f6bner bases of determinantal ideals. In International Congress on Mathematical Software. Springer, 354\u2013364."},{"key":"e_1_3_3_1_25_2","doi-asserted-by":"crossref","unstructured":"Himanee Narasimhan. 1986. The irreducibility of ladder determinantal varieties. Journal of Algebra 102 1 (1986) 162\u2013185.","DOI":"10.1016\/0021-8693(86)90134-1"},{"key":"e_1_3_3_1_26_2","doi-asserted-by":"crossref","unstructured":"Craige Schensted. 1961. Longest increasing and decreasing subsequences. Canadian Journal of Mathematics 13 (1961) 179\u2013191.","DOI":"10.4153\/CJM-1961-015-3"},{"key":"e_1_3_3_1_27_2","doi-asserted-by":"crossref","unstructured":"Bernd Sturmfels. 1990. Gr\u00f6bner bases and Stanley decompositions of determinantal rings. Mathematische Zeitschrift 205 1 (1990) 137\u2013144.","DOI":"10.1007\/BF02571229"},{"key":"e_1_3_3_1_28_2","volume-title":"Gr\u00f6bner Bases and Convex Polytopes","author":"Sturmfels Bernd","year":"1996","unstructured":"Bernd Sturmfels. 1996. Gr\u00f6bner Bases and Convex Polytopes. Vol.\u00a08. American Mathematical Soc."}],"event":{"name":"ISSAC '25: International Symposium on Symbolic and Algebraic Computation","sponsor":["SIGSAM ACM Special Interest Group on Symbolic and Algebraic Manipulation"],"location":"Guanajuato Mexico","acronym":"ISSAC '25"},"container-title":["Proceedings of the 2025 International Symposium on Symbolic and Algebraic Computation"],"original-title":[],"link":[{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3747199.3747558","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,10]],"date-time":"2025-11-10T11:39:30Z","timestamp":1762774770000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3747199.3747558"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,7,28]]},"references-count":27,"alternative-id":["10.1145\/3747199.3747558","10.1145\/3747199"],"URL":"https:\/\/doi.org\/10.1145\/3747199.3747558","relation":{},"subject":[],"published":{"date-parts":[[2025,7,28]]},"assertion":[{"value":"2025-11-10","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}