Combinatorial interpretations of continued fractions with multiple limit points
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This dissertation establishes an Euler-Minding type theorem for the continued fraction with numerator elements --1 and denominator elements 1 + bi, where bi is a sequence of indeterminants. This theorem is employed to derive new partition identities from Ramanujan's well-known q-continued fraction which diverges to three limit points. Continued fractions that diverge to two limits are also considered: alternating partitions studied by Andrews are shown to occur in this context, and a new proof of a result of Alladi is given.