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Bhattacharjee, Mandal and Bhattacharya on monochromatic union-closed families
Deep Bhattacharjee, Priyabrata Mandal and Ushashi Bhattacharya, Resolving Erdős–Ulam Monochromatic Union-Closed Family Conjectures, arXiv:2610.02833v1, 2 October 2026. The selected edition is the arXiv first version, available as the PDF and its accompanying arXiv TeX and HTML source files.
The preprint concerns monochromatic union-closed subfamilies of the power set of an n-element set. For two colors its Theorems 1.1 and 1.2 claim the superpolynomial lower and subexponential upper bounds asked for in Problem 1183. These assertions concern the union-closed function F; they do not determine the exact orders of F or of the function f for families also closed under intersection. The authors also supply a formalization, whose reported status is not an independent check here.
Reading boundary. The source identity, abstract and opening statements were read for acquisition. The proofs have not been examined here. This card records an unrefereed source and conveys no acceptance of its claims.
Terms. The arXiv record inspected on 2026-10-15 identifies the selected edition as CC BY 4.0.