论文标题
换档，九头蛇的持续分数和M呈隔板分区
Shift-plethysm, Hydra continued fractions, and m-distinct partitions
论文作者
论文摘要
我们介绍了九头蛇的持续分数，因为罗杰斯 - 拉马努扬的概括持续了分数，并用换档树木进行了组合解释。然后，我们表明可以将它们表示为M-Distinct分区生成函数的商，并以双重形式作为与M-1上限上限上升的组成函数的生成函数的商。我们根据其局部最小值获得新的生成功能，用于具有规定的上升集的分区以及具有规定的连续差异集的组成。
We introduce the hydra continued fractions, as a generalization of the Rogers-Ramanujan continued fractions, and give a combinatorial interpretation in terms of shift-plethystic trees. We then show it is possible to express them 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 rises 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.
