Two-Dimensional Palindromes and Their Properties

  • Manasi S. KulkarniEmail author
  • Kalpana Mahalingam
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10168)


A two-dimensional word (2D) is a rectangular finite array of letters from the alphabet \(\varSigma \). A 2D word is said to be a 2D palindrome if it is equal to its reverse image. In this paper, we study some combinatorial properties of 2D palindromes. In particular, we provide a sufficient condition under which a 2D word is said to be a 2D palindrome, discuss the necessary and sufficient condition under which a 2D word can be decomposed into 2D palindromes, and find the relation between the set of all 2D palindromes and the set of all 2D primitive words. We also show that the set of all 2D palindromes is not a recognizable language, and study a special class of 2D palindromes, namely 2D palindrome square words.


Combinatorics on words Two-Dimensional words Two-Dimensional palindromes Recognizable languages Primitivity Symmetry 


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Mathematics Indian Institute of Technology MadrasChennaiIndia

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