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The following question was posed by C. A. Nicol: Given an arbitrary set B of positive integers, find the extremal denominators of regular continued fractions with partial denominators from B, each element occurring a given number of times. Partial solutions have been given by T. S. Motzkin and E. G. Straus, and later by T. W. Cusick. We derive the general solutions from a purely combinatorial theorem about the set of permutations of a vector with components from an arbitrary linearly ordereddoi:10.2307/2044900 fatcat:io65vc7o4jbirfjm552rbfmxoq