On the Numbers of Palindromes

• Journal title : Kyungpook mathematical journal
• Volume 56, Issue 2,  2016, pp.349-355
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2016.56.2.349
Title & Authors
On the Numbers of Palindromes
Bang, Sejeong; Feng, Yan-Quan; Lee, Jaeun;

Abstract
For any integer $\small{n{\geq}2}$, each palindrome of n induces a circulant graph of order n. It is known that for each integer $\small{n{\geq}2}$, there is a one-to-one correspondence between the set of (resp. aperiodic) palindromes of n and the set of (resp. connected) circulant graphs of order n (cf. [2]). This bijection gives a one-to-one correspondence of the palindromes $\small{{\sigma}}$ with $gcd({\sigma}) Keywords compositions of n;palindromes;circulant graphs; Language English Cited by References 1. H. Baek, The number of aperiodic palindromes of n${\leq}\$ 127, available at http://chaos.cu.ac.kr/-tnad/.

2.
H. Baek. S. Bang, D. Kim and J. Lee, A bijection between aperiodic palindromes and connected circulant graphs, preprint.

3.
S. Heuhach, P. Chinn and R. Grimaldi, Rises, Levels, Drops and "+" Signs in Compositions: Extensions of a Paper by Alladi and Hoggatt, Fibonacci Quarterly 41(3)(1975), 229-239.

4.
N. J. A. Sloane, The On-Line Encyclopedia of Integer Sequences, http://oeis.org/A179519.