论文标题
由fibonacci单词构建的多元和图形
Polyominoes and graphs built from Fibonacci words
论文作者
论文摘要
我们介绍了$ k $ -benacci polyominoes，这是一个与二进制单词相关的新系列多洋粉，避免了$ k $连续$ 1 $的$，也称为广义$ k $ bonacci单词。多元群是非常引人入胜的对象，在组合学和计算机科学中被认为。对多支克斯的研究产生了丰富的组合思想来源。在本文中，我们研究了$ k $ bonacci多元的一些特性。具体而言，我们确定它们的递归结构，并使用此结构根据其区域，半层计和相应单词的长度进行枚举。我们还介绍了$ K $ -BONACCI图，然后我们获得了顶点和边缘总数，学位的分布以及具有汉密尔顿周期的$ K $ -BONACCI图的生成功能。
We introduce the $k$-bonacci polyominoes, a new family of polyominoes associated with the binary words avoiding $k$ consecutive $1$'s, also called generalized $k$-bonacci words. The polyominoes are very entrancing objects, considered in combinatorics and computer science. The study of polyominoes generates a rich source of combinatorial ideas. In this paper we study some properties of $k$-bonacci polyominoes. Specifically, we determine their recursive structure and, using this structure, we enumerate them according to their area, semiperimeter, and length of the corresponding words. We also introduce the $k$-bonacci graphs, then we obtain the generating functions for the total number of vertices and edges, the distribution of the degrees, and the total number of $k$-bonacci graphs that have a Hamiltonian cycle.
