Counting monochromatic solutions to diagonal Diophantine equations

Autor: Sean Prendiville

Publikováno v: Discrete Analysis (2021)

Counting monochromatic solutions to diagonal Diophantine equations, Discrete Analysis 2021:14, 47 pp. An important subfield of Ramsey theory concerns questions of the following type: for which systems of equations $E_1,\dots,E_k$ in variables $x_1,\

Externí odkaz: https://doaj.org/article/dd13bfc783fb44c29bdab055c349e571

Extremal Sidon sets are Fourier uniform, with applications to partition regularity

Autor: Miquel Ortega, Sean Prendiville

Generalising results of Erd\H{o}s-Freud and Lindstr\"om, we prove that the largest Sidon subset of a bounded interval of integers is equidistributed in Bohr neighbourhoods. We establish this by showing that extremal Sidon sets are Fourier-pseudorando

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e89d540dd3f76a23069eaee68df9c70d
https://eprints.lancs.ac.uk/id/eprint/181273/

On the Ramsey number of the Brauer configuration

Autor: Jonathan Chapman, Sean Prendiville

Publikováno v: Bulletin of the London Mathematical Society. 52:316-334

We obtain a double exponential bound in Brauer's generalisation of van der Waerden's theorem, which concerns progressions with the same colour as their common difference. Such a result has been obtained independently and in much greater generality by

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1e49afe097adc9de4a3ce1082e0b0b1d
https://doi.org/10.1112/blms.12327

Surveys in Combinatorics 2022

Autor: Anthony Nixon, Sean Prendiville

This volume contains eight survey articles by the invited speakers of the 29th British Combinatorial Conference, held at Lancaster University in July 2022. Each article provides an overview of recent developments in a current hot research topic in co

Improvements in Birch’s theorem on forms in many variables

Autor: Tim D Browning, Sean Prendiville

Publikováno v: Browning, T D & Prendiville, S M 2017, ' Improvements in Birch's theorem on forms in many variables ', Journal für die reine und angewandte Mathematik, vol. 2017, no. 731, pp. 203-234 . https://doi.org/10.1515/crelle-2014-0122

We show that a non-singular integral form of degree d is soluble over the integers if and only if it is soluble over ℝ {\mathbb{R}} and over ℚ p {\mathbb{Q}_{p}} for all primes p, provided that the form has at least ( d - 1 2 ⁢ d ) ⁢ 2 d {(d-

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a0c7bc1edb33cf6ff225d5232fb62d7a
https://doi.org/10.1515/crelle-2014-0122