We enumerate several classes of pattern-avoiding rectangulations. We establish bijective links with pattern-avoiding permutations, prove that their generating functions are algebraic, and confirm several conjectures by Merino and M\"utze. We also analyze a new class of rectangulations, called whirls, using a generating tree.

翻译：我们枚举了几类避免模式的矩形剖分。我们建立了与避免模式排列的双射联系，证明了其生成函数是代数的，并验证了Merino和Mütze的几个猜想。我们还使用生成树分析了一类新的矩形剖分，称为涡旋（whirls）。