Bounds on the frequency of 1 in the Kolakoski word

光滑二元词中的洗牌平方与Kolakoski序列

Shuffle squares in smooth binary words and the Kolakoski sequence

本文证明长度至少18且两字母出现偶数次的光滑二元词必为洗牌平方，并应用于Kolakoski序列，刻画其洗牌平方前缀的条件。

Smooth infinite words over $n$-letter alphabets having same remainder when divided by $n$

Brlek et al. (2008) studied smooth infinite words and established some results on letter frequency, recurrence, reversal and complementation for 2-letter alphabets having same parity. In this paper, we explore smooth infinite words over $n$-letter alphabet $\{a_1,a_2,...,a_n\}$, where $a_1<a_2<...<a_n$ are positive integers and have same remainder when divided by $n$. And let $a_i=n\cdot q_i+r,\;q_i\in N$ for $i=1,2,...,n$, where $r=0,1,2,...,n-1$. We use distinct methods to prove that (1) if $r=0$, the letters frequency of two times differentiable well-proportioned infinite words is $1/n$, wh…

二元字母表上平滑词的复杂度

The complexity of smooth words over binary alphabets

本文研究二元字母表上平滑词的因子复杂度，证明了有限平滑词是平滑词的因子，并证明了在偶数字母表上的复杂度阶，在任意二元字母表上的下界，改进了奇数字母表上的上界。

纯形态词中字母频率与因子频率的关系

Letter frequency vs factor frequency in pure morphic words

本文证明了纯形态词中若所有字母频率存在，则所有因子频率也存在，解决了Saari博士论文中的问题。

由子序列频率限制的二进制单词枚举

Enumerating binary words restricted by subsequence frequency

研究长度为\(n\)且恰好有\(k\)个子序列等于特定长度为\(\ell\)且有\(r\geq2\)个游程的二进制单词\(p\)的数量，证明其为\(n\)的至多\(\ell - r + 1\)次多项式，并给出相关上界。

二元字中的子序列频率

Subsequence frequency in binary words

该研究围绕二元字中子序列出现频率展开，推导小出现次数下的计数显式表达式，分析短游程子序列的最大出现次数，还探究计数序列的内部零点及单峰、对数凹性。