An integer linear programming model for tilings

IF 0.5 2区数学 Q4 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Journal of Mathematics and Music Pub Date : 2021-07-08 DOI:10.1080/17459737.2023.2180812

Gennaro Auricchio, L. Ferrarini, Greta Lanzarotto

引用次数: 3

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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平铺的整数线性规划模型

在本文中，我们提出了一个整数线性规划模型，其解是具有给定节奏a的非周期节奏平铺。我们展示了如何使用它来定义一个迭代算法，该算法在给定周期n时，找到具有给定节奏a的所有节奏平铺，并有效地检查了coveno - meyerowitz条件(T2)的必要性。最后，我们运行了几个实验来验证该模型的时间效率。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Mathematics and Music 数学-数学跨学科应用

CiteScore

1.90

自引率

18.20%

发文量

审稿时长

>12 weeks

期刊介绍： Journal of Mathematics and Music aims to advance the use of mathematical modelling and computation in music theory. The Journal focuses on mathematical approaches to musical structures and processes, including mathematical investigations into music-theoretic or compositional issues as well as mathematically motivated analyses of musical works or performances. In consideration of the deep unsolved ontological and epistemological questions concerning knowledge about music, the Journal is open to a broad array of methodologies and topics, particularly those outside of established research fields such as acoustics, sound engineering, auditory perception, linguistics etc.