2019/12/26 by Xizhi Liu, Liu, Xizhi
Computer Science · Engineering · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1912.11917
openalex publication_date 2019/12/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A triple system is cancellative if it does not contain three distinct sets A,B,C such that the symmetric difference of A and B is contained in C. We show that every cancellative triple system H that satisfies certain inequality between the sizes of H and its shadow must be structurally close to the balanced blowup of some Steiner triple system. Our result contains a stability theorem for cancellative triple systems due to Keevash and Mubayi as a special case. It also implies that the boundary of the feasible region of cancellative triple systems has infinitely many local maxima, thus giving the first example showing this phenomenon.