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The meridional rank conjecture posits equality between the bridge number $\beta$ and meridional rank $\mu$ of a link $L\subset S^3$. I will describe a diagram coloring technique – which amounts to finding quotients of link groups – by which we establish the conjecture for new infinite classes of links. We obtain upper bounds for $\beta$ via the Wirtinger number of L, a combinatorial equivalent of the bridge number. Matching lower bounds on $\mu$ are found using Coxeter quotients of $\pi_1(S^3\backslash L)$. As a corollary, we derive formulas for the bridge numbers for the links in question. Based on joint works with Blair, Baader-Blair, Baader-Blair-Misev.