论文标题
$ \ mathbb {q} $ - bonacci单词和数字
$\mathbb{Q}$-bonacci words and numbers
论文作者
论文摘要
我们提出了多步菲曲acci数字的奇怪概括。对于任何积极的有理$ Q $，我们列举了长度$ n $的二进制单词，其最大因素$ 0^a1^b $满足$ a = 0 $或$ aq> b $。当$ q $是整数时，我们重新发现了经典的多步斐济人数字：斐波那契，tribonacci，tetranacci等。当$ q $不是整数时，获得的复发关系就会连接到某些限制性整数组成。我们还讨论了这些单词的灰色代码，并可能对黄金比率进行新颖的概括。
We present a quite curious generalization of multi-step Fibonacci numbers. For any positive rational $q$, we enumerate binary words of length $n$ whose maximal factors of the form $0^a1^b$ satisfy $a = 0$ or $aq > b$. When $q$ is an integer we rediscover classical multi-step Fibonacci numbers: Fibonacci, Tribonacci, Tetranacci, etc. When $q$ is not an integer, obtained recurrence relations are connected to certain restricted integer compositions. We also discuss Gray codes for these words, and a possibly novel generalization of the golden ratio.
