The Riemann Hypothesis on Young's Lattice
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…
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