2025/02/18 by Tingzeng Wu, Wu, Tingzeng, Dong, Xiangshuai +2
Computer Science · Engineering · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Matrix Theory and Algorithms #Point processes and geometric inequalities #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2502.12787
openalex publication_date 2025/02/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let \mathscrU(n,τ) be the set of all \rm(0,1)-matrices of order n with exactly τ 0's. Brualdi et al. investigated the maximum permanents of all matrices in \mathscrU(n,τ)(R.A. Brualdi, J.L. Goldwasser, T.S. Michael, Maximum permanents of matrices of zeros and ones, J. Combin. Theory Ser. A 47 (1988) 207--245.). And they put forward an open problem to characterize the maximum permanents among all matrices in \mathscrU(n,τ). In this paper, we focus on the problem. And we characterize the maximum permanents of all matrices in \mathscrU(n,τ) when n2-3n≤τ≤ n2-2n-1. Furthermore, we also prove the maximum permanents of all matrices in \mathscrU(n,τ) when σ-kn≡0 (mod~k+1) and (k+1)n-σ≡0(mod~k), where σ=n2-τ, kn≤σ≤ (k+1)n and k is integer.