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Computational and Mathematical Methods in Medicine
Volume 2016, Article ID 5010316, 5 pages
http://dx.doi.org/10.1155/2016/5010316
Research Article

Compatibility and Conjugacy on Partial Arrays

1Department of Science and Humanity, Sathyabama University, Chennai, India
2Department of Mathematics, St. Joseph’s College of Engineering, Chennai, India

Received 27 March 2016; Revised 28 July 2016; Accepted 3 August 2016

Academic Editor: Qi Dai

Copyright © 2016 S. Vijayachitra and K. Sasikala. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Research in combinatorics on words goes back a century. Berstel and Boasson introduced the partial words in the context of gene comparison. Alignment of two genes can be viewed as a construction of two partial words that are said to be compatible. In this paper, we examine to which extent the fundamental properties of partial words such as compatbility and conjugacy remain true for partial arrays. This paper studies a relaxation of the compatibility relation called -compability. It also studies -conjugacy of partial arrays.