2016/09/23 by Jan Kristian Haugland, Haugland, Jan Kristian · 2 citations
Engineering · #00-02 (Primary) #11A-02 (Secondary) #FOS: Mathematics #General Mathematics (math.GM) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1609.08000
openalex publication_date 2016/09/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For a given partition of (1, 2, ..., 2n) into two disjoint subsets A and B with n elements in each, consider the maximum number of times any integer occurs as the difference between an element of A and an element of B. The minimum value of this maximum (over all partitions) is denoted by M(n). By a result of Swinnerton-Dyer, one way to estimate lim M(n)/n from above is to give step functions that describe the density of A, say, throughout the interval [1, 2n] for a large n rather than looking for explicit partitions. A step function that improves the upper bound from 0.382002... to 0.380926... is given.