https://discreteanalysisjournal.com/ Discrete Analysis is a mathematical journal with an emphasis on areas of mathematics that are broadly related to additive combinatorics. en 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 Mon, 06 Oct 2025 08:10:44 +0000 The maximum, minimum and typical number of symmetries of regular bipartite multigraphs are determined. https://doi.org/10.19086/da.144894 https://discreteanalysisjournal.com/article/144894-regular-bipartite-multigraphs-have-many-but-not-too-many-symmetries Thu, 02 Oct 2025 08:11:19 +0000 Characterizations are given of groups that are highly quasirandom, in the sense that the dimension of every non-trivial irreducible representation is of power size. https://doi.org/10.19086/da.144893 https://discreteanalysisjournal.com/article/144893-quasirandom-and-quasisimple-groups Tue, 30 Sep 2025 08:07:49 +0000 A Kelley-Meka-strength bound is obtained for the maximum density of a subset of a 2-dimensional grid that contains no triple of the form (x,y), (x,y+d), (x+d,y') with d>0. https://doi.org/10.19086/da.144040 https://discreteanalysisjournal.com/article/144040-strong-bounds-for-skew-corner-free-sets Mon, 29 Sep 2025 07:35:43 +0000 An optimal 2-dimensional estimate for the finite-fields version of the Furstenberg problem would imply an optimal n-dimensional estimate for all n. https://doi.org/10.19086/da.144860 https://discreteanalysisjournal.com/article/144860-exceptional-set-estimate-in-prime-fields-dimension-two-implies-higher-dimensions