Counting words satisfying the rhythmic oddity property
Abstract
This paper describes an enumeration of all words having a combinatoric property called "rhythmic oddity property"named rop-words.\ This property was introduced by Simha Aron in the 1990s. The set of rop-words is not a subset of the set of Lyndon words, but is very closed. We show that there is a bijection between some necklaces and rop-words. This leads to a formula for counting the rop-words of a given length. Keywords: Combinatoric on words. Lyndon words. Rhythmic oddity. Music formalization
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