On the Maximum Number of Distinct Palindromic Sub-arrays

摘要

We investigate the maximum number of distinct palindromic sub-arrays in a two-dimensional finite word over a finite alphabet Σ. For any finite array in Σ~(m×n), we find an upper bound for the number of distinct palindromic sub-arrays and improve it by giving a tight bound on the maximum number of distinct palindromes in an array in Σ~(2×n) for |Σ| =2. We then, propose a better upper bound for any finite array in Σ~(m×n).