论文标题
自然的培养单词避免连续模式
A natural bijection for contiguous pattern avoidance in words
论文作者
论文摘要
两个单词$ p $和$ q $由相同数量的长度-n $单词避免，对于所有$ n $，恰好是$ p $和$ q $具有相同的边框长度时。该定理的先前证明使用生成功能，但没有提供明确的培养。我们为所有对$ p，q $提供了相同的适当边界的族果证明，从一组避免$ p $的单词中建立了自然的培养，到避免$ q $的单词集。
Two words $p$ and $q$ are avoided by the same number of length-$n$ words, for all $n$, precisely when $p$ and $q$ have the same set of border lengths. Previous proofs of this theorem use generating functions but do not provide an explicit bijection. We give a bijective proof for all pairs $p, q$ that have the same set of proper borders, establishing a natural bijection from the set of words avoiding $p$ to the set of words avoiding $q$.
