PALINDROMES IN INFINITE TERNARY WORDS

We study infinite words u over an alphabet A satisfyingthe property P : P(n) + P(n + 1) = 1 +#A for any n ∈ N, whereP(n) denotes the number of palindromic factors of length n occurringin the language of u. We study also infinite words satisfying a strongerproperty PE : every palindrome of u has exactly one palindromicextension in u. For binary words, the properties P and PE coincideand these properties characterize Sturmian words, i.e., words with thecomplexity C(n) = n + 1 for any n ∈ N. In this paper, we focus onternary infinite words with the language closed under reversal. Forsuch words u, we prove that if C(n) = 2n + 1 for any n ∈ N, then usatisfies the property P and moreover u is rich in palindromes. Alsoa sufficient condition for the property PE is given. We construct a worddemonstrating that P on a ternary alphabet does not imply PE