# Problem 12: Conjugate Palindromes

The problem is related to the two operations on words consisting of reversing a word and taking one of its conjugate. The operations are essentially incompatible in the sense that only a few conjugates of a word are also its reverse.

To examine the situation, we consider palindromes that are conjugates of each other.

What is the maximal number of palindromes in the conjugacy class of a word?
Consider the primitive root of two conjugate palindromes.

## References

• C. Guo, J. Shallit, and A. M. Shur. On the combinatorics of palindromes and antipalindromes. CoRR, abs/1503.09112, 2015.