Here we provide three new presentations of Coxeter groups of type A, B, and D using prefix reversals (pancake flips) as generators. The purpose of these presentations is to advance the algebraic underpinnings of the pancake problem. We prove these presentations are of their respective groups by using Tietze transformations on the presentations to recover the well known presentations with generators that are adjacent transpositions. We also provide a statement for the classic pancake problem for type D.

中文翻译：

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使用前缀反转生成器表示 A、B 和 D 类型的 Coxeter 组

在这里，我们使用前缀反转（煎饼翻转）作为生成器，提供了类型A、B和D的 Coxeter 组的三个新演示。这些演讲的目的是推进煎饼问题的代数基础。我们通过对演示文稿使用 Tietze 变换来证明这些演示文稿属于它们各自的组，以使用相邻转置的生成器来恢复众所周知的演示文稿。我们还为类型D的经典煎饼问题提供了一个陈述。