2025/09/24 by Keane Maverick Irawan, Irawan, Keane Maverick
Mathematics · #05D05 #11B13 #11B30 #Advanced Topology and Set Theory #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Limits and Structures in Graph Theory #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2509.20568
openalex publication_date 2025/09/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the minimax problem for restricted two-fold self-sumsets in k-colorings of ℤn. For primes p with 2≤ k≤ p we determine the exact minimum max\0, 2\lceil p/k\rceil-3\. For general n (with m=\lceil n/k\rceil) we bound the optimum between a size term min\p(n), 2m-3\ and a periodicity term f(n/q(n,k)), and show these bounds are tight when 2m-3≤ p(n) or f(n/q(n,k))≤ min\p(n), 2m-3\. We further prove a stability inequality and a threshold theorem that force concentration in a single subgroup coset near the periodic scale. In the prime case with m≥ 5 and 2m-3