论文标题
关于保存圆锥形丰富性的形态学
On morphisms preserving palindromic richness
论文作者
论文摘要
众所周知，每个长度$ n $的单词最多都包含$ n+1 $不同的单词。有限的单词是一个具有最大alind骨因子数量的词。自然可以将全文丰富的定义扩展到无限的单词。 Sturmian单词和死记硬背的互补对称序列形成了两类二进制富单词，而Episturmian单词和单词编码对称$ D $ -Interval交换转换为我们提供了其他较大字母的其他示例。在本文中，我们寻找了自由单型的形态，这使我们能够从已知的丰富单词中构造新的丰富词。我们专注于类$ p_ {ret} $中的形态。该类包含字母表上的形态学和满足特定的pelindromicity属性：对于班级中的每个形态$φ$，都有一个palindrome $ w $，因此$φ（a）w $是每个字母$ a $ a $ $ w $ $ w $的第一个完整的返回单词。我们表征了$ p_ {ret} $形态，这些形态保留了二进制字母上的丰富度。我们还研究标志着$ p_ {ret} $形态上作用于字母，并带有更多字母。特别是我们表明，每个arnoux-rauzy的形态都是与$ p_ {ret} $类中的形态相结合的，并且保留了丰富性。
It is known that each word of length $n$ contains at most $n+1$ distinct palindromes. A finite rich word is a word with maximal number of palindromic factors. The definition of palindromic richness can be naturally extended to infinite words. Sturmian words and Rote complementary symmetric sequences form two classes of binary rich words, while episturmian words and words coding symmetric $d$-interval exchange transformations give us other examples on larger alphabets. In this paper we look for morphisms of the free monoid, which allow us to construct new rich words from already known rich words. We focus on morphisms in Class $P_{ret}$. This class contains morphisms injective on the alphabet and satisfying a particular palindromicity property: for every morphism $φ$ in the class there exists a palindrome $w$ such that $φ(a)w$ is a first complete return word to $w$ for each letter $a$. We characterize $P_{ret}$ morphisms which preserve richness over a binary alphabet. We also study marked $P_{ret}$ morphisms acting on alphabets with more letters. In particular we show that every Arnoux-Rauzy morphism is conjugated to a morphism in Class $P_{ret}$ and that it preserves richness.
