Some new results on palindromic factors of billiard words

Abstract

For heuristic reasons billiard words may have more palindromic factors than any other words. Many results are already known, concerning the palindromic factors and the palindromic prefixes of Sturmian words and billiard words on two letters. We give general results concerning multidimensional billiard words, which describe very different situations. In some cases, these words have arbitrary long palindromic prefix factors. In other cases, at the opposite, they have finitely many distinct palindromic factors. © Springer-Verlag Berlin Heidelberg 2005.