Random palindromes: multivariate generating function and Bernoulli density Original Research Article

Consider a finite alphabet with a probability distribution p. We study the probability δ(p) of obtaining a palindrome in a finite time by independent draws. Using a Mahler equation for an associated generating function, we give a closed-form expression for δ(p). Moreover we describe completely the cases where δ(p) has value less than 1, in connection with the singularities of the generating function. Except for the case of a one or two letters alphabet it is found that δ(p) is always less than 1.