Algebraic Matroids in Action. Issue 3 (15th March 2020)

• Record Type: Journal Article
• Authors: Rosen, Zvi; Sidman, Jessica; Theran, Louis
• Is Part Of: American Mathematical Monthly. Volume 127:Issue 3(2020)
• Page Start: 199
• Page End: 216
• Publication Date: 2020-03-15
• Subjects: Primary 05B35; Mathematics -- Periodicals; 510.5
• DOI: 10.1080/00029890.2020.1689781
• Languages: English
• ISSNs: 0002-9890

Abstract

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.