2025/08/31 by Yorick Herrmann, Herrmann, Yorick, Hill, Connor +7 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Graph Theory Research #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2509.00792
openalex publication_date 2025/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A More Sums Than Difference (MSTD) set is a finite set of integers A where the cardinality of its sumset, A+A, is greater than the cardinality of its difference set, A-A. Since addition is commutative while subtraction isn't, it was conjectured that MSTD sets are rare. As Martin and O'Bryant proved a small (but positive) percentage are MSTD, it is natural to ask what additional properties can we impose on a chain of MSTD sets; in particular, can we construct a sequence of sets alternating between being MSTD and More Difference Than Sums (MDTS) where each properly contains the previous? We provide several such constructions; the first are trivial and proceed by filling in all missing elements from the minimum to maximum elements of A, while the last is a more involved construction that prohibits adding any such elements.