Abstract
The “rhythmic oddity property” (rop) was introduced by ethnomusicologist Simha Aron in the 1990s. The set of rop words is the set of words over the alphabet \(\{2,3\}\) satisfying the rhythmic oddity property. It 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. We also propose a generalization of rop words over a finite alphabet \(\mathcal {A} \subset \{1,2,\ldots ,s\}\) for some integer \(s \ge 2\). The enumeration of these generalized rop words is still open.
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