Counting words satisfying the rhythmic oddity property
Combinatorics
2017-07-07 v2
Abstract
This paper describes an enumeration of all words having a combinatoric property called "rhythmic oddity property"named \emph{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. \textsc{Keywords:} Combinatoric on words. Lyndon words. Rhythmic oddity. Music formalization
Cite
@article{arxiv.1607.07175,
title = {Counting words satisfying the rhythmic oddity property},
author = {Franck Jedrzejewski},
journal= {arXiv preprint arXiv:1607.07175},
year = {2017}
}
Comments
7 pages, 1 figure