The Billaud Conjecture for alphabet size 4

IF 1 4区计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS

Information and Computation Pub Date : 2025-08-20 DOI:10.1016/j.ic.2025.105342

Szymon Łopaciuk , Daniel Reidenbach

引用次数: 0

Abstract

The Billaud Conjecture, first stated in 1993, is a fundamental problem on finite words and their heirs, i.e., the words obtained by a projection deleting a single letter. The conjecture states that every morphically primitive word, i.e., a word that is not a fixed point of any non-identity morphism, has at least one morphically primitive heir. The correctness of the conjecture has so far been established in a few special cases, which mainly restrict the alphabet size. In this paper we give a proof for the next such case, i.e., for alphabet size 4.

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字母表大小为4的比劳猜想

1993年首次提出的比劳猜想是一个关于有限词及其后继词的基本问题，即通过删除单个字母的投影得到的词。该猜想指出，每一个词形原词，即不是任何非同一性词形的不动点的词，至少有一个词形原继承人。到目前为止，这个猜想的正确性已经在一些特殊情况下得到了证实，这些情况主要限制了字母表的大小。本文给出了下一种情况的证明，即对于字母大小为4的情况。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Information and Computation 工程技术-计算机：理论方法

CiteScore

2.30

自引率

0.00%

发文量

119

审稿时长

140 days

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