{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T08:44:39Z","timestamp":1773391479178,"version":"3.50.1"},"reference-count":22,"publisher":"Springer Science and Business Media LLC","issue":"S2","license":[{"start":{"date-parts":[[2022,9,21]],"date-time":"2022-09-21T00:00:00Z","timestamp":1663718400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2022,9,21]],"date-time":"2022-09-21T00:00:00Z","timestamp":1663718400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Combinatorica"],"published-print":{"date-parts":[[2022,12]]},"DOI":"10.1007\/s00493-021-4815-z","type":"journal-article","created":{"date-parts":[[2022,9,21]],"date-time":"2022-09-21T17:03:23Z","timestamp":1663779803000},"page":"1357-1384","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Polynomial Schur\u2019s Theorem"],"prefix":"10.1007","volume":"42","author":[{"given":"Hong","family":"Liu","sequence":"first","affiliation":[]},{"given":"P\u00e9ter P\u00e1l","family":"Pach","sequence":"additional","affiliation":[]},{"given":"Csaba","family":"S\u00e1ndor","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,9,21]]},"reference":[{"key":"4815_CR1","doi-asserted-by":"publisher","first-page":"63","DOI":"10.1090\/conm\/065\/891243","volume":"65","author":"V Bergelson","year":"1987","unstructured":"V. Bergelson: Ergodic Ramsey theory. In Logic and combinatorics (Arcata, Calif., 1985), Contemp. Math. 65 (1987), 63\u201387, Amer. Math. Soc., Providence, RI, 1987.","journal-title":"Contemp. Math."},{"key":"4815_CR2","doi-asserted-by":"publisher","first-page":"725","DOI":"10.1090\/S0894-0347-96-00194-4","volume":"9","author":"V Bergelson","year":"1996","unstructured":"V. Bergelson and A. Leibman: Polynomial extensions of van der Waerden\u2019s and Szemer\u00e9di\u2019s theorems, J. Amer. Math. Soc. 9 (1996), 725\u2013753.","journal-title":"J. Amer. Math. Soc."},{"key":"4815_CR3","unstructured":"S. Chow, S. Lindqvist and S. Prendiville: Rado\u2019s criterion over squares and higher powers, J. Euro. Math. Soc., to appear."},{"key":"4815_CR4","doi-asserted-by":"publisher","first-page":"425","DOI":"10.1007\/s00493-012-2697-9","volume":"32","author":"P Csikv\u00e1ri","year":"2012","unstructured":"P. Csikv\u00e1ri, K. Gyarmati and A. S\u00e1rk\u00f6zy: Density and Ramsey type results on algebraic equations with restricted solution sets, Combinatorica 32 (2012), 425\u2013449.","journal-title":"Combinatorica"},{"key":"4815_CR5","doi-asserted-by":"publisher","first-page":"84","DOI":"10.1016\/j.aim.2017.11.003","volume":"324","author":"M Di Nasso","year":"2018","unstructured":"M. Di Nasso and L. Luperi Baglini: Ramsey properties of nonlinear Diophantine equations, Advances in Mathematics 324 (2018), 84\u2013117.","journal-title":"Advances in Mathematics"},{"key":"4815_CR6","doi-asserted-by":"publisher","first-page":"204","DOI":"10.1007\/BF02813304","volume":"31","author":"H Furstenberg","year":"1977","unstructured":"H. Furstenberg: Ergodic behavior of diagonal measures and a theorem of Szemer\u00e9di on arithmetic progressions, J. d\u2019Analyse Math. 31 (1977), 204\u2013256.","journal-title":"J. d\u2019Analyse Math."},{"key":"4815_CR7","doi-asserted-by":"publisher","first-page":"579","DOI":"10.4153\/CJM-2017-036-1","volume":"71","author":"B Green","year":"2019","unstructured":"B. Green and S. Lindqvist: Monochromatic solutions to x + y = z2, Canadian Journal of Mathematics 71 (2019), 579\u2013605.","journal-title":"Canadian Journal of Mathematics"},{"key":"4815_CR8","first-page":"48","volume":"5","author":"B Green","year":"2016","unstructured":"B. Green and T. Sanders: Monochromatic sums and products, Discrete Analysis 5 (2016), 48.","journal-title":"Discrete Analysis"},{"key":"4815_CR9","doi-asserted-by":"publisher","first-page":"213","DOI":"10.1017\/S0963548305007169","volume":"15","author":"A Khalafallah","year":"2006","unstructured":"A. Khalafallah and E. Szemer\u00e9di: On the Number of Monochromatic Solutions of x + y = z2, Combinatorics, Probability and Computing 15 (2006), 213\u2013227.","journal-title":"Combinatorics, Probability and Computing"},{"key":"4815_CR10","doi-asserted-by":"publisher","first-page":"459","DOI":"10.1007\/BF01174162","volume":"58","author":"M Kneser","year":"1958","unstructured":"M. Kneser: Absch\u00e4tzungen der asymptotischen Dichte von Summenmengen, Math. Zeitschr. 58 (1958), 459\u2013484.","journal-title":"Math. Zeitschr."},{"key":"4815_CR11","unstructured":"S. Lindqvist: Partition regularity for generalised Fermat equations, Combinatorica, to appear."},{"key":"4815_CR12","first-page":"199","volume":"78","author":"F Mertens","year":"1874","unstructured":"F. Mertens: Ein Beitrag zur analytischen Zahlentheorie, J. reine angew. Math. 78 (1874), 199\u2013245.","journal-title":"J. reine angew. Math."},{"key":"4815_CR13","doi-asserted-by":"publisher","first-page":"1069","DOI":"10.4007\/annals.2017.185.3.10","volume":"185","author":"J Moreira","year":"2017","unstructured":"J. Moreira: Monochromatic sums and products in N, Annals of Mathematics 185 (2017), 1069\u20131090.","journal-title":"Annals of Mathematics"},{"key":"4815_CR14","doi-asserted-by":"publisher","first-page":"1113","DOI":"10.1112\/blms.12207","volume":"50","author":"P P Pach","year":"2018","unstructured":"P. P. Pach: Monochromatic solutions to x + y = z2 in the interval [N, cN4], Bulletin of the London Mathematical Society 50 (2018), 1113\u20131116.","journal-title":"Bulletin of the London Mathematical Society"},{"key":"4815_CR15","first-page":"A23","volume":"8","author":"C Pohoata","year":"2008","unstructured":"C. Pohoata: Boole\u2019s formula as a consequence of Lagrange\u2019s interpolation formula, Integers 8 (2008), A23.","journal-title":"Integers"},{"key":"4815_CR16","doi-asserted-by":"publisher","first-page":"424","DOI":"10.1007\/BF01188632","volume":"36","author":"R Rado","year":"1933","unstructured":"R. Rado: Studien zur Kombinatorik, Math. Z. 36 (1933), 424\u2013470.","journal-title":"Math. Z."},{"key":"4815_CR17","doi-asserted-by":"publisher","first-page":"R19","DOI":"10.37236\/1357","volume":"5","author":"A Robertson","year":"1998","unstructured":"A. Robertson and D. Zeilberger: A 2-coloring of [1, N] can have (1\/22)N2+O(N) monochromatic Schur triples, but not less!, Electronic Journal of Combinatorics 5 (1998), R19.","journal-title":"Electronic Journal of Combinatorics"},{"key":"4815_CR18","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1007\/BF01896079","volume":"31","author":"A S\u00e1rk\u00f6zy","year":"1978","unstructured":"A. S\u00e1rk\u00f6zy: On difference sets of sequences of integers. I, Acta Math. Acad. Sci. Hungar. 31 (1978), 125\u2013149.","journal-title":"Acta Math. Acad. Sci. Hungar."},{"key":"4815_CR19","doi-asserted-by":"publisher","first-page":"855","DOI":"10.1006\/eujc.1999.0297","volume":"20","author":"T Schoen","year":"1999","unstructured":"T. Schoen: The number of monochromatic Schur triples, Euro. J. Combinatorics 20 (1999), 855\u2013866.","journal-title":"Euro. J. Combinatorics"},{"key":"4815_CR20","first-page":"114","volume":"14","author":"I Schur","year":"1916","unstructured":"I. Schur: \u00dcber die Kongruenz xm + ym \u2261 zm (mod p), Jahresber. Dtsch. Math.-Ver. 14 (1916), 114\u2013117.","journal-title":"Jahresber. Dtsch. Math.-Ver."},{"key":"4815_CR21","doi-asserted-by":"publisher","first-page":"199","DOI":"10.4064\/aa-27-1-199-245","volume":"27","author":"E Szemer\u00e9di","year":"1975","unstructured":"E. Szemer\u00e9di: On sets of integers containing no k elements in arithmetic progression, Acta Arithmetica 27 (1975), 199\u2013245.","journal-title":"Acta Arithmetica"},{"key":"4815_CR22","first-page":"212","volume":"15","author":"B L van der Waerden","year":"1927","unstructured":"B. L. van der Waerden: Beweis einer baudetschen vermutung, Nieuw. Arch. Wisk. 15 (1927), 212\u2013216.","journal-title":"Nieuw. Arch. Wisk."}],"container-title":["Combinatorica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00493-021-4815-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00493-021-4815-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00493-021-4815-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,2,2]],"date-time":"2023-02-02T16:33:55Z","timestamp":1675355635000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00493-021-4815-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,9,21]]},"references-count":22,"journal-issue":{"issue":"S2","published-print":{"date-parts":[[2022,12]]}},"alternative-id":["4815"],"URL":"https:\/\/doi.org\/10.1007\/s00493-021-4815-z","relation":{},"ISSN":["0209-9683","1439-6912"],"issn-type":[{"value":"0209-9683","type":"print"},{"value":"1439-6912","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,9,21]]},"assertion":[{"value":"9 March 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 October 2021","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 September 2022","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}