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After relevant definitions, some motivation, and some results from the literature, we will show that cylindrical decompositions correspond exactly to pairs of an ordinary decomposition and a colored decomposition into different parts. According to the remaining time, we will explain how to obtain the generator functions of cylindrical decompositions in different sections and give examples. This study is a joint work with Halime Ömrüuzun Seyrek (https://arxiv.org/abs/2308.14514).   

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