{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,30]],"date-time":"2026-03-30T13:19:43Z","timestamp":1774876783659,"version":"3.50.1"},"reference-count":36,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2021,8,31]],"date-time":"2021-08-31T00:00:00Z","timestamp":1630368000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,8,31]],"date-time":"2021-08-31T00:00:00Z","timestamp":1630368000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Combinatorica"],"published-print":{"date-parts":[[2021,12]]},"DOI":"10.1007\/s00493-020-4523-0","type":"journal-article","created":{"date-parts":[[2021,8,31]],"date-time":"2021-08-31T14:04:40Z","timestamp":1630418680000},"page":"839-872","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Equiangular Lines in Low Dimensional Euclidean Spaces"],"prefix":"10.1007","volume":"41","author":[{"given":"Gary R. W.","family":"Greaves","sequence":"first","affiliation":[]},{"given":"Jeven","family":"Syatriadi","sequence":"additional","affiliation":[]},{"given":"Pavlo","family":"Yatsyna","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,8,31]]},"reference":[{"key":"4523_CR1","doi-asserted-by":"publisher","first-page":"62","DOI":"10.1016\/j.laa.2018.07.019","volume":"557","author":"J Azarija","year":"2018","unstructured":"J. Azarija and T. Marc: There is no (75, 32, 10, 16) strongly regular graph, Linear Algebra Appl. 557 (2018), 62\u201383.","journal-title":"Linear Algebra Appl."},{"key":"4523_CR2","doi-asserted-by":"publisher","first-page":"294","DOI":"10.1002\/jcd.21696","volume":"28","author":"J Azarija","year":"2020","unstructured":"J. Azarija and T. Marc: There is no (95, 40, 12, 20) strongly regular graph, J. Combin. Des. 28 (2020), 294\u2013306.","journal-title":"J. Combin. Des."},{"key":"4523_CR3","doi-asserted-by":"publisher","first-page":"179","DOI":"10.1007\/s00222-017-0746-0","volume":"211","author":"I Balla","year":"2018","unstructured":"I. Balla, F. Draxler, P. Keevash and B. Sudakov: Equiangular lines and spherical codes in Euclidean space, Invent. Math. 211 (2018), 179\u2013212.","journal-title":"Invent. Math."},{"key":"4523_CR4","doi-asserted-by":"publisher","first-page":"549","DOI":"10.1137\/15M1036920","volume":"30","author":"B Bukh","year":"2016","unstructured":"B. Bukh: Bounds on equiangular lines and on related spherical codes, SIAM J. Discrete Math. 30 (2016), 549\u2013554.","journal-title":"SIAM J. Discrete Math."},{"key":"4523_CR5","series-title":"\u0152uvres compl\u00e8tes, IIi\u00e8me S\u00e9rie","volume-title":"Sur l\u2019\u00e9quation \u00e0 l\u2019aide de laquelle on d\u00e9termine les in\u00e9galit\u00e9s s\u00e9culaires des mouvements des plan\u00e8tes","author":"A-L Cauchy","year":"1829","unstructured":"A.-L. Cauchy: Sur l\u2019\u00e9quation \u00e0 l\u2019aide de laquelle on d\u00e9termine les in\u00e9galit\u00e9s s\u00e9culaires des mouvements des plan\u00e8tes, in: \u0152uvres compl\u00e8tes, IIi\u00e8me S\u00e9rie, Gauthier-Villars, Paris, 1829."},{"key":"4523_CR6","series-title":"Encyclopedia of Mathematics and its Applications","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139086547","volume-title":"Eigenspaces of graphs","author":"D Cvetkovi\u0107","year":"1997","unstructured":"D. Cvetkovi\u0107, P. Rowlinson and S. Simi\u0107: Eigenspaces of graphs, Encyclopedia of Mathematics and its Applications, vol. 66, Cambridge University Press, Cambridge, 1997."},{"key":"4523_CR7","unstructured":"P. B. Denton, S. J. Parke, T. Tao and X. Zhang: Eigenvectors from Eigenvalues: a survey of a basic identity in linear algebra, arXiv:1908.03795, 2019."},{"key":"4523_CR8","first-page":"1","volume":"124","author":"J Farkas","year":"1902","unstructured":"J. Farkas: Theorie der einfachen Ungleichungen, Journal f\u00fcr die reine und angewandte Mathematik 124 (1902), 1\u201327.","journal-title":"Journal f\u00fcr die reine und angewandte Mathematik"},{"key":"4523_CR9","first-page":"118","volume":"112","author":"S Fisk","year":"2005","unstructured":"S. Fisk: A very short proof of Cauchy\u2019s interlace theorem for eigenvalues of Hermitian matrices, Amer. Math. Monthly 112 (2005), 118.","journal-title":"Amer. Math. Monthly"},{"key":"4523_CR10","doi-asserted-by":"publisher","first-page":"285","DOI":"10.1016\/0095-8956(81)90046-0","volume":"30","author":"C D Godsil","year":"1981","unstructured":"C. D. Godsil and B. D. McKay: Spectral conditions for the reconstructibility of a graph, J. Combin. Theory Ser. B 30 (1981), 285\u2013289.","journal-title":"J. Combin. Theory Ser. B"},{"key":"4523_CR11","doi-asserted-by":"publisher","first-page":"810","DOI":"10.1016\/j.aim.2018.03.024","volume":"330","author":"A Glazyrin","year":"2018","unstructured":"A. Glazyrin and W.-H. Yu: Upper bounds for s-distance sets and equiangular lines, Adv. Math. 330 (2018), 810\u2013833.","journal-title":"Adv. Math."},{"key":"4523_CR12","unstructured":"G. R. W. Greaves: SageMath notebook containing computations from the paper \u201cEquiangular lines in low dimensional Euclidean spaces\u201d, https:\/\/github.com\/grwgrvs\/interlacing-characteristic-polynomials\/."},{"key":"4523_CR13","doi-asserted-by":"publisher","first-page":"31","DOI":"10.1016\/j.laa.2017.09.008","volume":"536","author":"G R W Greaves","year":"2018","unstructured":"G. R. W. Greaves: Equiangular line systems and switching classes containing regular graphs, Linear Algebra Appl. 536 (2018), 31\u201351.","journal-title":"Linear Algebra Appl."},{"key":"4523_CR14","doi-asserted-by":"publisher","first-page":"208","DOI":"10.1016\/j.jcta.2015.09.008","volume":"138","author":"G R W Greaves","year":"2016","unstructured":"G. R. W. Greaves, J. Koolen, A. Munemasa and F. Sz\u00f6ll\u0151si: Equiangular lines in Euclidean spaces, J. Combin. Theory Ser. A 138 (2016), 208\u2013235.","journal-title":"J. Combin. Theory Ser. A"},{"key":"4523_CR15","doi-asserted-by":"publisher","first-page":"3041","DOI":"10.1090\/mcom\/3433","volume":"88","author":"G R W Greaves","year":"2019","unstructured":"G. R. W. Greaves and P. Yatsyna: On equiangular lines in 17 dimensions and the characteristic polynomial of a Seidel matrix, Math. Comp. 88 (2019), 3041\u20133061.","journal-title":"Math. Comp."},{"key":"4523_CR16","first-page":"355","volume":"22","author":"J Haantjes","year":"1948","unstructured":"J. Haantjes: Equilateral point-sets in elliptic two- and three-dimensional spaces, Nieuw Arch. Wiskd. 22 (1948), 355\u2013362.","journal-title":"Nieuw Arch. Wiskd."},{"key":"4523_CR17","doi-asserted-by":"publisher","first-page":"257","DOI":"10.1016\/S1063-5203(03)00023-X","volume":"14","author":"R W Heath","year":"2003","unstructured":"R. W. Heath and T. Strohmer: Grassmannian frames with applications to coding and communication, Appl. Comput. Harmon. Anal. 14(3) (2003), 257\u2013275.","journal-title":"Appl. Comput. Harmon. Anal."},{"key":"4523_CR18","doi-asserted-by":"publisher","first-page":"157","DOI":"10.1080\/00029890.2004.11920060","volume":"111","author":"S-G Hwang","year":"2004","unstructured":"S.-G. Hwang: Cauchy\u2019s interlace theorem for eigenvalues of Hermitian matrices, Amer. Math. Monthly 111 (2004), 157\u2013159.","journal-title":"Amer. Math. Monthly"},{"key":"4523_CR19","unstructured":"Z. Jiang, J. Tidor, Y. Yao, S. Zhang and Y. Zhao: Equiangular lines with a fixed angle, arXiv:1907.12466, 2019."},{"key":"4523_CR20","doi-asserted-by":"publisher","first-page":"2479","DOI":"10.1137\/19M1248881","volume":"33","author":"E King","year":"2019","unstructured":"E. King and X. Tang: New upper bounds for equiangular lines by pillar decomposition, SIAM J. Discrete Math. 33 (2019), 2479\u20132508.","journal-title":"SIAM J. Discrete Math."},{"key":"4523_CR21","doi-asserted-by":"crossref","unstructured":"D. de Laat, F. C. Machado, F. M. de Oliveira Filho and F. Vallentin: k-point semidefinite programming bounds for equiangular lines, Math. Program. (2021).","DOI":"10.1007\/s10107-021-01638-x"},{"key":"4523_CR22","doi-asserted-by":"publisher","first-page":"494","DOI":"10.1016\/0021-8693(73)90123-3","volume":"24","author":"P W H Lemmens","year":"1973","unstructured":"P. W. H. Lemmens and J. J. Seidel: Equiangular lines, J. Algebra 24(3) (1973), 494\u2013512.","journal-title":"J. Algebra"},{"key":"4523_CR23","doi-asserted-by":"publisher","first-page":"272","DOI":"10.1016\/j.laa.2019.12.002","volume":"588","author":"Y-C Lin","year":"2020","unstructured":"Y.-C. Lin and W.-H. Yu: Saturated configuration and new large construction of equiangular lines, Linear Algebra Appl. 588 (2020), 272\u2013281.","journal-title":"Linear Algebra Appl."},{"key":"4523_CR24","doi-asserted-by":"publisher","first-page":"335","DOI":"10.1016\/S1385-7258(66)50038-5","volume":"28","author":"J H van Lint","year":"1966","unstructured":"J. H. van Lint and J. J. Seidel: Equilateral point sets in elliptic geometry, Indag. Math. 28 (1966), 335\u2013348.","journal-title":"Indag. Math."},{"key":"4523_CR25","unstructured":"Wolfram Research, Inc., Mathematica, Version Number 10.0, Champaign, IL (2014)."},{"key":"4523_CR26","series-title":"Lecture Notes in Comput. Sci.","doi-asserted-by":"publisher","first-page":"327","DOI":"10.1007\/978-3-540-24847-7_25","volume-title":"Algorithmic number theory","author":"J F McKee","year":"2004","unstructured":"J. F. McKee and C. J. Smyth: Salem numbers of trace \u22122 and traces of totally positive algebraic integers, Algorithmic number theory, 327\u2013337, Lecture Notes in Comput. Sci., 3076, Springer, Berlin, 2004."},{"key":"4523_CR27","doi-asserted-by":"publisher","first-page":"96","DOI":"10.1016\/j.ejc.2015.11.003","volume":"53","author":"T Okuda","year":"2016","unstructured":"T. Okuda and W.-H. Yu: A new relative bound for equiangular lines and nonexistence of tight spherical designs of harmonic index 4, European J. Combin. 53 (2016), 96\u2013103.","journal-title":"European J. Combin."},{"key":"4523_CR28","unstructured":"The PARI Group, PARI\/GP version 2.10, Univ. Bordeaux, http:\/\/pari.math.u-bordeaux.fr\/."},{"key":"4523_CR29","doi-asserted-by":"publisher","first-page":"115","DOI":"10.6028\/jres.072B.015","volume":"72","author":"R C Thompson","year":"1968","unstructured":"R. C. Thompson: Principal submatrices V: Some results concerning principal submatrices of arbitrary matrices, J. Res. Nat. Bur. Standards Sect. B 72 (1968), 115\u2013125.","journal-title":"J. Res. Nat. Bur. Standards Sect. B"},{"key":"4523_CR30","volume-title":"Graphs and two-graphs","author":"J J Seidel","year":"1974","unstructured":"J. J. Seidel: Graphs and two-graphs, in: Proc. 5th Southeastern Conf. on Combinatorics, Graph Theory, and Computing, Utilitas Mathematica Publishing Inc., Winnipeg, Canada, 1974."},{"key":"4523_CR31","volume-title":"Handbook of Incidence Geometry","author":"J J Seidel","year":"1995","unstructured":"J. J. Seidel: Discrete non-Euclidean geometry, in: Buekenhout (ed.), Handbook of Incidence Geometry, Elsevier Science, Amsterdam, The Netherlands (1995)."},{"key":"4523_CR32","unstructured":"N. J. A. Sloane (editor): The On-Line Encyclopedia of Integer Sequences, Published electronically at https:\/\/oeis.org\/."},{"key":"4523_CR33","unstructured":"W. A. Stein et al.: Sage Mathematics Software (Version 8.8), The Sage Development Team, 2010, http:\/\/www.sagemath.org\/."},{"key":"4523_CR34","doi-asserted-by":"publisher","first-page":"120","DOI":"10.1007\/s00454-017-9933-4","volume":"61","author":"F Sz\u00f6ll\u0151si","year":"2019","unstructured":"F. Sz\u00f6ll\u0151si: A remark on a construction of D. S. Asche, Discrete Comput. Geom. 61 (2019), 120\u2013122.","journal-title":"Discrete Comput. Geom."},{"key":"4523_CR35","doi-asserted-by":"publisher","first-page":"257","DOI":"10.1112\/plms\/s3-35.2.257","volume":"35","author":"D E Taylor","year":"1977","unstructured":"D. E. Taylor: Regular 2-graphs, Proc. London Math. Soc. 35 (1977), 257\u2013274.","journal-title":"Proc. London Math. Soc."},{"key":"4523_CR36","doi-asserted-by":"publisher","first-page":"908","DOI":"10.1137\/16M109377X","volume":"31","author":"W-H Yu","year":"2017","unstructured":"W.-H. Yu: New bounds for equiangular lines and spherical two-distance sets, SIAM J. Discrete Math. 31 (2017), 908\u2013917.","journal-title":"SIAM J. Discrete Math."}],"container-title":["Combinatorica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00493-020-4523-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00493-020-4523-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00493-020-4523-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,12,31]],"date-time":"2021-12-31T00:03:35Z","timestamp":1640909015000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00493-020-4523-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,8,31]]},"references-count":36,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2021,12]]}},"alternative-id":["4523"],"URL":"https:\/\/doi.org\/10.1007\/s00493-020-4523-0","relation":{},"ISSN":["0209-9683","1439-6912"],"issn-type":[{"value":"0209-9683","type":"print"},{"value":"1439-6912","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,8,31]]},"assertion":[{"value":"22 March 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 November 2020","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"31 August 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}