A new measure of asymmetry of binary words

TL;DR

This paper introduces a novel measure of asymmetry for binary words based on minimal deletions needed to achieve symmetry, providing bounds for this measure.

Contribution

It defines a new asymmetry measure for binary words and derives upper and lower bounds for it, advancing understanding of word symmetry properties.

Findings

Established upper and lower bounds for the asymmetry measure

Provided a formal definition of the asymmetry measure

Analyzed properties of binary words related to symmetry

Abstract

A binary word is symmetric if it is a palindrome or an antipalindrome. We define a new measure of asymmetry of a binary word equal to the minimal number of letters of the word whose deleting from the word yields a symmetric word and obtain upper and lower estimations of this measure.