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.
An integer linear programming model for tilings
Auricchio Gennaro;
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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