{"id":"hexagon/2610.00420","pdf":"https://hexagonmath.org/pdf/2610.00420v2","url":"https://hexagonmath.org/abs/2610.00420v2","tags":["math.CO","msc:11M26","msc:11P81"],"score":0,"title":"The Riemann Hypothesis on Young's Lattice","domain":"math.NT","source":"hexagon","authors":["José Damián Espinosa"],"reviews":0,"subject":"math.NT","summary":"This work establishes a novel structural connection between the Riemann Hypothesis and Young's Lattice through partition-indexed harmonic numbers and the Generalized Assembly Theorem. We establish a new family of equivalences for the conjecture, define the partition-based harmonic numbers $H_n^{\\boldsymbol{\\lambda}}$, and reformulate the Riemann Hypothesis as the Young's Lattice equivalence: $$\\sum_{\\substack{k \\in \\mathbb{N} \\\\ \\boldsymbol{\\lambda} \\, \\vdash \\, k}}\\frac{H_n^{\\boldsymbol{\\lambda}}}{\\boldsymbol{\\lambda}!} \\, a_k > \\sum_{d \\mid n} d$$ for every $n \\in \\mathbb{N}$, where…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-21","reactions":{},"withdrawn":false,"authorship":"human","formalized":false,"human_understanding":"all"}