The syntactic monoid of θ-free palindromic words

IF 1.3 3区数学 Q3 MATHEMATICS, APPLIED

Advances in Applied Mathematics Pub Date : 2025-09-09 DOI:10.1016/j.aam.2025.102964

Kalpana Mahalingam

引用次数: 0

Abstract

In this paper, we consider words that are free of special type of palindromes, inspired by Watson-Crick complementarity in DNA sequences which we call Watson-Crick palindromic free words or θ-palindromic free words, when θ is an antimorphic involution that incorporates the notion of Watson-Crick complementarity of DNA sequences. We discuss certain algebraic properties of the set of all words that avoids θ-palindromes. We give a complete characterization of the syntactic monoid of the language consisting of all θ-palindromic free words over a given alphabet. We also study the ideals of the corresponding syntactic semigroup obtained using Green's relations. Our results also hold for the more general case, where the Watson-Crick complementarity function is replaced by an arbitrary antimorphic involution.

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无θ回文词的句法单一性

本文从DNA序列中的沃森-克里克互补性的启发，考虑不存在特殊类型回文的词，我们称之为沃森-克里克回文自由词或θ-回文自由词，当θ是包含DNA序列沃森-克里克互补性概念的反同构对合时。我们讨论避免θ-回文的所有词的集合的某些代数性质。我们给出了由给定字母表上的所有θ-回文自由词组成的语言的句法一元的完整表征。我们还研究了利用格林关系得到的相应的句法半群的理想。我们的结果也适用于更一般的情况，其中Watson-Crick互补函数被任意反同构对合所取代。

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

Advances in Applied Mathematics 数学-应用数学

CiteScore

2.00

自引率

9.10%

发文量

审稿时长

85 days

期刊介绍： Interdisciplinary in its coverage, Advances in Applied Mathematics is dedicated to the publication of original and survey articles on rigorous methods and results in applied mathematics. The journal features articles on discrete mathematics, discrete probability theory, theoretical statistics, mathematical biology and bioinformatics, applied commutative algebra and algebraic geometry, convexity theory, experimental mathematics, theoretical computer science, and other areas. Emphasizing papers that represent a substantial mathematical advance in their field, the journal is an excellent source of current information for mathematicians, computer scientists, applied mathematicians, physicists, statisticians, and biologists. Over the past ten years, Advances in Applied Mathematics has published research papers written by many of the foremost mathematicians of our time.