2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/227094We consider the following problem: Given a nested sum expression, find a sum representation such that the nested depth is minimal. We obtain a symbolic summation framework that solves this problem for sums defined, e.g., over hypergeometric, $q$-hypergeometric or mixed hypergeometric expressions. Recently, our methods have found applications in quantum field theory.To appear in Clay Mathematics ProceedingsSymbolic ComputationCombinatoricsNumber Theorytext