Palindromic complexity of trees

TL;DR

This paper explores the palindromic complexity of labeled finite trees, analyzing the number of distinct palindromic paths and proposing bounds on their quantity within the tree's language.

Contribution

It introduces the concept of palindromic complexity for trees and offers initial bounds and insights into the maximum number of palindromes in a tree's language.

Findings

Proposed an upper bound on the number of distinct palindromes in a tree's language.

Analyzed the structure of labeled trees to understand palindrome distribution.

Provided theoretical insights into palindromic complexity in tree structures.

Abstract

We consider finite trees with edges labeled by letters on a finite alphabet $\varSigma$. Each pair of nodes defines a unique labeled path whose trace is a word of the free monoid $\varSigma^*$. The set of all such words defines the language of the tree. In this paper, we investigate the palindromic complexity of trees and provide hints for an upper bound on the number of distinct palindromes in the language of a tree.