Abstract
We introduce the hydra continued fractions, as a generalization of the Rogers–Ramanujan continued fractions in the context of noncommutative series, and give them a combinatorial interpretation in terms of shift-plethystic trees. We show it is possible to express an m−1 headed hydra continued fraction as a quotient of m-distinct partition generating functions, and in its dual form as a quotient of the generating functions of compositions with contiguous differences upper bounded by m−1. We obtain new generating functions for compositions according to their local minima, for partitions with a prescribed set of rises, and for compositions with prescribed sets of contiguous differences.
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