Bubble-Flip---A New Generation Algorithm for Prefix Normal Words

We present a new recursive generation algorithm for prefix normal words.These are binary strings with the property that no substring has more 1s thanthe prefix of the same length. The new algorithm uses two operations on binarystrings, which exploit certain properties of prefix normal words in a smartway. We introduce infinite prefix normal words and show that one of theoperations used by the algorithm, if applied repeatedly to extend the string,produces an ultimately periodic infinite word, which is prefix normal and whoseperiod's length and density we can predict from the original word.