2014/11/02 by Daniil Rudenko, Rudenko, Daniil
Mathematics · #52C20 (Primary) 52C20 (Secondary) #Advanced Combinatorial Mathematics #Algebraic Geometry and Number Theory #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.1411.0285
openalex publication_date 2014/11/02 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Monsky proved that a square cannot be dissected into an odd number of triangles of equal area. Stein conjectured that the same holds for any polygon whose edges can be paired into parallel and equal-length segments. We prove Stein's conjecture under an assumption that all triangle vertices have rational coordinates. Our result is derived from a more general property of trivalent graphs equipped with a ℚ2-valued flow.