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ENUMERATING NECKLACES WITH TRANSITIONS
Bulletin of the Australian Mathematical Society ( IF 0.6 ) Pub Date : 2021-05-11 , DOI: 10.1017/s0004972721000307 FRANCESCO BIANCONI , EMANUELE BRUGNOLI
Bulletin of the Australian Mathematical Society ( IF 0.6 ) Pub Date : 2021-05-11 , DOI: 10.1017/s0004972721000307 FRANCESCO BIANCONI , EMANUELE BRUGNOLI
Necklaces are the equivalence classes of words under the action of the cyclic group. Let a transition in a word be any change between two adjacent letters modulo the word’s length. We present a closed-form solution for the enumeration of necklaces in n beads, k colours and t transitions. We show that our result provides a more general solution to the problem of counting alternating (proper) colourings of the vertices of a regular n -gon.
中文翻译:
枚举带有过渡的项链
项链是词在循环群作用下的等价类。让单词中的转换为两个相邻字母之间的任何变化,以单词的长度为模。我们提出了一个封闭形式的项链枚举解决方案n 珠子,ķ 颜色和吨 过渡。我们表明,我们的结果为计算规则顶点的交替(正确)着色问题提供了更通用的解决方案n -贡。
更新日期:2021-05-11
中文翻译:
枚举带有过渡的项链
项链是词在循环群作用下的等价类。让单词中的转换为两个相邻字母之间的任何变化,以单词的长度为模。我们提出了一个封闭形式的项链枚举解决方案