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.

我们介绍了hydra连续分数，作为非交换级数上下文中Rogers-Ramanujan连续分数的推广，并根据频移多变树对它们进行了组合解释。我们证明有可能表达一个$米-\mathrm{1个}$ 头水合连续分数为 $米$-distinct分区生成函数，并以对偶形式表示具有连续差异且上限为的合成的生成函数的商 $米-\mathrm{1个}$。我们根据成分的局部最小值，具有规定的上升集的分区以及具有规定的连续差异集的成分获得新的生成函数。