https://discreteanalysisjournal.com/ Discrete Analysis is a mathematical journal with an emphasis on areas of mathematics that are broadly related to additive combinatorics. en Mon, 27 Jul 2026 08:01:21 +0000 A method is developed for using Ramsey theorems to deduce more powerful Ramsey theorems. The method has many consequences and is used to solve several open problems. https://doi.org/10.19086/da.165253 https://discreteanalysisjournal.com/article/165253-composite-ramsey-theorems-via-trees Tue, 21 Jul 2026 08:15:07 +0000 For each fixed d, the Erdős-Ginzburg-Ziv constant of the dth power of the cyclic group of order p is determined asymptotically as p tends to infinity. https://doi.org/10.19086/da.165216 https://discreteanalysisjournal.com/article/165216-convex-geometry-and-the-erdos-ginzburg-ziv-problem Thu, 16 Jul 2026 09:38:00 +0000 For each h and for sufficiently large k, the set of possible cardinalities of the h-fold sumset hA, when A is a set of size k, is determined. https://doi.org/10.19086/da.165102 https://discreteanalysisjournal.com/article/165102-possible-sizes-of-sumsets Thu, 16 Jul 2026 09:34:00 +0000 A group presentation is constructed that has few generators and relations and that has a stability property that provides a key step in the proof that MIP*=RE. https://doi.org/10.19086/da.154623 https://discreteanalysisjournal.com/article/154623-efficiently-stable-presentations-from-error-correcting-codes Fri, 19 Dec 2025 11:24:43 +0000 A sharp lower bound is obtained for the number of ways of representing a rational number as an Egyptian fraction with denominators at most n. https://doi.org/10.19086/da.154329 https://discreteanalysisjournal.com/article/154329-a-question-of-erdos-and-graham-on-egyptian-fractions Wed, 17 Dec 2025 09:55:08 +0000 This paper studies how the analytic and partition rank of a tensor can change when the underlying field is extended. https://doi.org/10.19086/da.145807 https://discreteanalysisjournal.com/article/145807-stability-of-ranks-under-field-extensions Fri, 10 Oct 2025 06:58:53 +0000 Certain natural configurations are universally optimal with respect to the hexagonal lattice, which lends support to the conjecture that they all are. https://doi.org/10.19086/da.144978 https://discreteanalysisjournal.com/article/144978-universally-optimal-periodic-configurations-in-the-plane Thu, 09 Oct 2025 07:37:10 +0000 An elementary proof is given of the fact that the slice rank of a tensor of rank 3 is bounded above by a constant times its analytic rank. https://doi.org/10.19086/da.145198 https://discreteanalysisjournal.com/article/145198-slice-rank-and-analytic-rank-for-trilinear-forms Wed, 08 Oct 2025 07:03:31 +0000 A function-field variant of Marton's conjecture, otherwise known as the polynomial Freiman Ruzsa theorem for finite fields, is formulated and proved. https://doi.org/10.19086/da.145176 https://discreteanalysisjournal.com/article/145176-a-polynomial-freiman-ruzsa-inverse-theorem-for-function-fields Tue, 07 Oct 2025 08:14:37 +0000 The number of vertices needed to guarantee a colour-avoiding tight monotone path in every r-coloured complete k-uniform hypergraph is exponentially smaller than the number needed for a monochromatic path. https://doi.org/10.19086/da.145175 https://discreteanalysisjournal.com/article/145175-color-avoidance-for-monotone-paths