2011/02/13 by В. И. Данилов, Danilov, Vladimir I., Alexander V. Karzanov +3 · 1 citation
Computer Science · Mathematics · #05C75 #05E99 #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Combinatorics (math.CO) #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1102.2578
openalex publication_date 2011/02/13 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
Adapting Lindström's well-known construction, we consider a wide class of functions which are generated by flows in a planar acyclic directed graph whose vertices (or edges) take weights in an arbitrary commutative semiring. We give a combinatorial description for the set of "universal" quadratic relations valid for such functions. Their specializations to particular semirings involve plenty of known quadratic relations for minors of matrices (e.g., Plücker relations) and the tropical counterparts of such relations. Also some applications and related topics are discussed.