Computing linear systems on metric graphs. (July 2018)

• Record Type: Journal Article
• Authors: Lin, Bo
• Is Part Of: Journal of symbolic computation. Volume 87(2018)
• Page Start: 54
• Page End: 67
• Publication Date: 2018-07
• Subjects: Metric graph -- Linear system -- Anchor cell -- f-vector; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2017.05.007
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: The linear system | D | of a divisor D on a metric graph has the structure of a cell complex. We introduce the anchor divisors and anchor cells in it – they serve as the landmarks for us to compute the f-vector of the complex and find all cells in the complex. A linear system can also be identified as a tropical convex hull of rational functions. We compute its extremal generators using the landmarks. We apply these methods to some examples – namely the canonical linear systems of some small trivalent graphs.