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The arithmetic one is based on the Fibonacci numeration system. We further show how to generate the floor words induced by the iterations using word-mappings and characterize them using the Fibonacci numeration system. We also exhibit an infinite array of such sequences.<\/jats:p>","DOI":"10.1137\/090758994","type":"journal-article","created":{"date-parts":[[2010,5,26]],"date-time":"2010-05-26T18:52:18Z","timestamp":1274899938000},"page":"570-588","source":"Crossref","is-referenced-by-count":8,"title":["Complementary Iterated Floor Words and the Flora Game"],"prefix":"10.1137","volume":"24","author":[{"given":"Aviezri S.","family":"Fraenkel","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2010,5,26]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","unstructured":"J.P. Allouche and J. 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