In this paper, we propose an integer linear programming model whose solutions are the aperiodic rhythms tiling with a given rhythm A. We show how it can be used to define an iterative algorithm that, given a period n, finds all the rhythms which tile with a given rhythm A and also to efficiently check the necessity of the Coven-Meyerowitz condition (T2). To conclude, we run several experiments to validate the time efficiency of the model.
Auricchio, G., Ferrarini, L., Lanzarotto, G. (2023). An integer linear programming model for tilings. JOURNAL OF MATHEMATICS & MUSIC, 17(3), 514-530 [10.1080/17459737.2023.2180812].
An integer linear programming model for tilings
Ferrarini L.;Lanzarotto G.
2023
Abstract
In this paper, we propose an integer linear programming model whose solutions are the aperiodic rhythms tiling with a given rhythm A. We show how it can be used to define an iterative algorithm that, given a period n, finds all the rhythms which tile with a given rhythm A and also to efficiently check the necessity of the Coven-Meyerowitz condition (T2). To conclude, we run several experiments to validate the time efficiency of the model.
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