Voir la notice de l'article provenant de la source Cambridge University Press
@article{10_1017_fmp_2024_19,
author = {Matt Bowen and Marcin Sabok},
title = {Monochromatic products and sums in the rationals},
journal = {Forum of Mathematics, Pi},
publisher = {mathdoc},
volume = {12},
year = {2024},
doi = {10.1017/fmp.2024.19},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1017/fmp.2024.19/}
}
Matt Bowen; Marcin Sabok. Monochromatic products and sums in the rationals. Forum of Mathematics, Pi, Tome 12 (2024). doi: 10.1017/fmp.2024.19
[BG20] and , ‘On the interplay between additive and multiplicative largeness and its combinatorial applications’, J. Combin. Theory Ser. A 172(2020), 105203, 60.Google Scholar | DOI
[BL96] and , ‘Polynomial extensions of van der Waerden's and Szemeredi's theorems’, J. Am. Math. Soc., 9(1996), 725–753.Google Scholar | DOI
[BM17] and , ‘Ergodic theorem involving additive and multiplicative groups of a field and patterns’, Ergod. Theory Dyn. Syst. 37(3) (2017), 673–692.Google Scholar | DOI
[BM18] and , ‘Measure preserving actions of affine semigroups and patterns’, Ergod. Theory Dyn. Syst. 38(2) (2018), 473–498.Google Scholar | DOI
[Bow22] , ‘Monochromatic products and sums in -colorings of ’, Preprint, 2012, .Google Scholar | arXiv
[Cil12] , ‘Combinatorial problems in finite fields and Sidon sets’, Combinatorica 32(5) (2012), 497–511.Google Scholar | DOI
[FK91] and , ‘A density version of the Hales–Jewett theorem’, J. Anal. Math. 57(1) (1991), 64–119.Google Scholar | DOI
[FW78] and , ‘Topological dynamics and combinatorial number theory’, J. Anal. Math. 34(1) (1978), 61–85.Google Scholar | DOI
[Gre69] , ‘Invariant means on topological groups and their applications’, in Van Nostrand Mathematical Studies Series, No. 16 (Van Nostrand Reinhold Company, New York, 1969), iii–113.Google Scholar
[GRS91] , and , Ramsey Theory, vol. 20 (John Wiley & Sons, New York, 1991), xi–193.Google Scholar
[GS16] and , ‘Monochromatic sums and products’, Discrete Anal. (2016), 613.Google Scholar
[Han13] , ‘Capturing forms in dense subsets of finite fields’, Acta Arith. 160(3) (2013), 277–284.Google Scholar | DOI
[HIL23] , and , ‘Some new results on monochromatic sums and products in the rationals’, N. Y. J. Math. 29 (2023), 301–322.Google Scholar
[Hin74] , ‘Finite sums from sequences within cells of a partition of ’, J. Comb. Theory Ser. A 17 (1974), 1–11.Google Scholar | DOI
[Hin79] , ‘Partitions and sums and products of integers’, Trans. Am. Math. Soc. 247 (1979), 227–245.Google Scholar | DOI
[HS12] and , ‘Algebra in the Stone-Čech compactification’, in Theory and Applications, second revised and extended edition (De Gruyter Textbook, Walter de Gruyter & Co., Berlin, 2012), i–577.Google Scholar
[Mor13] , ‘On patterns in large sets of countable fields’, blog post (2013) https://joelmoreira.wordpress.com/2013/08/03/on-xyxy-patterns-in-large-sets-of-countable-fields/.Google Scholar
[Mor17] , ‘Monochromatic sums and products in ’, Ann. Math. (2017), 1069–1090.Google Scholar
[Qua23] (Quanta), ‘Coloring by numbers reveals arithmetic patterns in fractions’, (March, 2023), https://www.quantamagazine.org/coloring-by-numbers-reveals-arithmetic-patterns-in-fractions-20230315/.Google Scholar
[Sch16] , ‘Über die Kongruenz (mod )’, Jahresbericht der Deutschen Math. Verein. 25 (1916), 114–117.Google Scholar
[Shk10] , ‘On monochromatic solutions of some nonlinear equations in ’, Mat. Zametki 88(4) (2010), 625–634.Google Scholar | DOI
[Sze75] , ‘On sets of integers containing no elements in arithmetic progression’, Acta Arith. 27 (1975), 199–245.Google Scholar | DOI
[Tod10] , ‘Introduction to Ramsey spaces’, in Annals of Mathematics Studies, vol. 174 (Princeton University Press, Princeton, NJ, 2010), 1–296.Google Scholar
[TZ12] and , ‘A course in model theory’, in Lecture Notes in Logic, no. 40 (Cambridge University Press, 2012), i–248.Google Scholar
[Wae27] , ‘Beweis einer baudetschen Vermutung’, Nieuw. Arch. Wisk. 15 (1927), 212–216.Google Scholar
[Xia22] , ‘Monochromatic quotients, products and polynomial sums in the rationals’, Preprint, 2022, .Google Scholar | arXiv
Cité par Sources :