2015/07/09 by Ercan Altınışık, Altınışık, Ercan, Alî Keskin +7
Computer Science · Mathematics · #11C39 #15A18 #15A23 #15B36 #15B48 #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Matrix Theory and Algorithms #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #math.CO #math.SP #msc:11C39 #msc:15A18 #msc:15A23 #msc:15B36 #msc:15B48
paper · pdf · doi:10.48550/arxiv.1507.05112
11 pages
arxiv created 2015/07/09 · openalex publication_date 2015/07/09 · arxiv updated 2015/07/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let Kn be the set of all n× n lower triangular (0,1)-matrices with each diagonal element equal to 1, Ln = \ YYT: Y∈ Kn\ and let cn = minZ∈ Ln \lbrace μn(1)(Z):μn(1) (Z) is the smallest eigenvalue of Z \rbrace . The Ilmonen-Haukkanen-Merikoski conjecture (the IHM conjecture) states that cn is equal to the smallest eigenvalue of Y0Y0T, where (Y0)ij=\lbrace 0 · if i<j, 1 · if i=j, \frac1-(-1)i+j2 · if i>j. . In this paper we present a proof of this conjecture. In our proof we use an inequality for spectral radii of nonnegative matrices.