论文标题
线性复发和排列的字符串：灰色代码
Strings from linear recurrences and permutations: a Gray code
论文作者
论文摘要
每个积极增加的整数序列$ \ {a_n \} _ {n \ geq 0} $可以用作数字系统，通过合适的系数字符串来表示每个非负整数。我们分析了$ k $的斐波那契序列，导致二进制字符串避免$ 1^k $。我们证明了长度$ n $的字符串的set％$ f_n^{（k）} $之间的两次培养，$ s_ {n+1}的排列集（321,312,23 \ ldots（k+1）1）$。最后，基于这些字符串的已知灰色代码，我们为$ s_ {n+1}定义了一个灰色代码（321,312,23 \ ldots（k+1）1）$，其中两个连续的排列因相邻的换位而不同。
Each positive increasing integer sequence $\{a_n\}_{n\geq 0}$ can serve as a numeration system to represent each non-negative integer by means of suitable coefficient strings. We analyse the case of $k$-generalized Fibonacci sequences leading to the binary strings avoiding $1^k$. We prove a bijection between the set %$F_n^{(k)}$ of strings of length $n$ and the set of permutations of $S_{n+1}(321,312,23\ldots(k+1)1)$. Finally, basing on a known Gray code for those strings, we define a Gray code for $S_{n+1}(321,312,23\ldots(k+1)1)$, where two consecutive permutations differ by an adjacent transposition.
