HV-Palindromes in Two-Dimensional Words

Abstract

A two-dimensional (2D) word is a 2D palindrome if it is equal to its reverse and it is an HV-palindrome if all its columns and rows are 1D palindromes. We characterize such words and study some of their combinatorial and structural properties. We also find the number of possible palindromic conjugates of a 2D word. We investigate an upper bound on the number of distinct non-empty HV-palindromic subwords in any finite 2D word, thus, proving the conjecture given by Anisiu et al. We also identify the minimum number of HV-palindromic subwords in an infinite 2D word over a finite alphabet.