Palindromes in two-dimensional Words

04/25/2019

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by   Kalpana Mahalingam, et al.

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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 study some combinatorial and structural properties of HV-palindromes and its comparison with 2D palindromes. We investigate the maximum number number of distinct non-empty HV-palindromic sub-arrays in any finite 2D word, thus, proving the conjecture given by Anisiua et al. We also find the least number of HV-palindromes in an infinite 2D word over a finite alphabet size q.