论文标题
原始单词与非主要产品的组合特性
Combinatorial Properties of primitive words with Non-primitive Product
论文作者
论文摘要
令$ \ mathcal {a} $为尺寸$ n \ ge 2 $的字母。在本文中，我们对原始单词的完整说明$ p \ neq q $上的字母$ \ mathcal {a} $ size $ n \ geq2 $的大小$ n \ geq2 $，这样$ pq $是非主要的，$ | p | p | = 2 | q | $。特别是，如果$ l $是一个积极的整数，我们计算了所有夫妻$（p，q）$（p，q）$（p，q）的$ \ mathcal {e}（l，\ mathcal {a}）$的基数。然后，我们为这种基数及其渐近行为提供了组合公式，因为$ l $或$ n $属于无限。
Let $\mathcal{A}$ be an alphabet of size $n\ge 2$. In this paper, we give a complete description of primitive words $p\neq q$ over an alphabet $\mathcal{A}$ of size $n\geq2$ such that $pq$ is non-primitive and $|p|=2|q|$. In particular, if $l$ is s a positive integer, we count the cardinality of the set $\mathcal{E}(l,\mathcal{A})$ of all couples $(p,q)$ of primitive words such that $|p|=2|q|=2l$ and $pq$ is non-primitive. Then we give a combinatorial formula for this cardinality and its asymptotic behavior, as $l$ or $n$ goes to infinity.
