Convex geometry and the Erdős–Ginzburg–Ziv problem: Theorem 1.2
A Lean 4 formalization of Theorem 1.2 of Dmitrii Zakharov's Convex geometry and the Erdős–Ginzburg–Ziv problem. For every fixed positive dimension d, as p tends to infinity through the primes, the Erdős–Ginzburg–Ziv constant s(F_p^d) satisfies s(F_p^d) = p w(F_p^d) + o(p), where w is the weak Erdős–Ginzburg–Ziv constant. Supporting proofs include the convex-flag Helly and centerpoint theorems, flag decomposition lemma, balanced convex combinations, relative set expansion, and the polynomial method bound for w. This submission covers Theorem 1.2 and its upper-bound formulation, not every…
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