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A complete solution to the biased Alon-Krivelevich-Spencer-Szabó criterion problem for the discrepancy game Scaffolds for Higher Tropical Grassmannians: Foundations Krahn-Szegő type inequalities for graphs $\boldsymbol{2}$-Neighbor Bootstrap Percolation on Odd Graphs Modular inequalities and Alexander polynomials of pencil type conic-line arrangements Counterexamples regarding elementary symmetric partitions Bounds on Multiple $b$-Burst Deletion-Correcting Codes The mex statistic on combinatorial structures Proper Additive Edge Colorings of Regular Graphs Off-diagonal Ramsey numbers Semi-inducibility of 4-vertex graphs A Structural Condition on Point Sets with Few Distinct Dot Products A quantum N-dimer model Möbius transforms and Shapley values for vector-valued functions on weighted directed acyclic multigraphs Well quasi-order and atomicity for combinatorial structures under consecutive orders The Permanent Rank of a Matrix (Part Three) Note on the Additive Basis Conjecture Complexity of the Zero Set of a Matrix Schubert Ideal The existence of unexpected automorphisms in direct product graphs Reconstruction of oriented matroids from Varchenko-Gelfand algebras Addition theorems for Ziegler pairs of hyperplane arrangements Combinatorial proofs of Petrie Pieri rule and Plethystic Pieri rule Asymptotic structure. III. Excluding a fat tree Asymptotic structure. V. The coarse Menger conjecture in bounded path-width Word-Representable Co-Bipartite Graphs: Vertex Ordering, Representation Number, Speed, and Entropy Borel Kernels in Borel Directed Graphs Large induced subgraphs with prescribed degree parity Maya-Tupi graphs: a generalization of split graphs Recursions, Trains, Trees, and Combinatorial Rod Set Algebra Sufficient minimum degree conditions for the existence of highly connected or edge-connected subgraphs Ramsey numbers for 1-degenerate 3-graphs Bipartite graphs with minimum degree at least 15 are antimagic A coarse Halin Grid Theorem with applications to quasi-transitive, locally finite graphs Bounds on the game isolation number and exact values for paths and cycles Minors of non-hamiltonian polyhedra and the Herschel family Triangle-free subsets of the $r$-distance graph of the hypercube Notes on sum-free sets in abelian groups When are Hopf algebras determined by integer sequences? 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On the number of sum-free subsets of the square grid
Anubhab Ghosal · 2025-10-17 · via math.CO updates on arXiv.org

Generalising the Cameron--Erdős conjecture to two dimensions, Elsholtz and Rackham conjectured that the number of sum-free subsets of $[n]^2$ is $2^{0.6n^2+O(n)}$. We prove their conjecture.

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