Algebraic Matroids in Action
Algebraic Matroids in Action
复制标题
实际的代数拟阵
DOI：
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
Louis Theran
中科院分区：
文献类型：
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作者：
Zvi Rosen;J. Sidman;Louis Theran
近年来，各种代数独立性的概念在应用数学的许多领域中已经成为一个中心和统一的主题，包括代数统计和杆与关节框架的刚性理论。在这些设置中，基本问题是确定某些未知数在代数上依赖于给定数据的程度。这反过来又引起了人们对代数拟阵的兴趣，代数拟阵是代数(独立)依赖的组合形式。我们给出了一个完整的代数拟阵的介绍，并举例说明了它们的潜在应用。
Abstract In recent years, various notions of algebraic independence have emerged as a central and unifying theme in a number of areas of applied mathematics, including algebraic statistics and the rigidity theory of bar-and-joint frameworks. In each of these settings, the fundamental problem is to determine the extent to which certain unknowns depend algebraically on given data. This has, in turn, led to a resurgence of interest in algebraic matroids, which are the combinatorial formalism for algebraic (in)dependence. We give a self-contained introduction to algebraic matroids together with examples highlighting their potential application.