论文标题
多维持续分数的组合特性
Combinatorial properties of multidimensional continued fractions
论文作者
论文摘要
数学对象组合特性的研究是一个非常重要的研究领域，从这个意义上讲，对持续的部分进行了深入研究。然而，多维持续分数是由雅各比引起的算法引起的概括，到目前为止，已经对这种意义进行了很少的研究。在本文中，我们提出了对多维持续分数收敛的组合解释，以计算一些特定的瓷砖，从而推广了一些对经典持续分数的结果。
The study of combinatorial properties of mathematical objects is a very important research field and continued fractions have been deeply studied in this sense. However, multidimensional continued fractions, which are a generalization arising from an algorithm due to Jacobi, have been poorly investigated in this sense, up to now. In this paper, we propose a combinatorial interpretation of the convergents of multidimensional continued fractions in terms of counting some particular tilings, generalizing some results that hold for classical continued fractions.
