2018/04/04 by Trairat Jantaramas, Jantaramas, Trairat, Somphong Jitman +3
Mathematics · #11B25 #15A33 #15B05 #Combinatorics (math.CO) #FOS: Mathematics #Rings and Algebras (math.RA) #math.CO #math.RA #msc:11B25 #msc:15A33 #msc:15B05
paper · pdf · doi:10.48550/arxiv.1804.01196
arxiv created 2018/04/04 · arxiv updated 2018/04/05
Due to their rich algebraic structures and various applications, circulant matrices have been of interest and continuously studied. In this paper, the notions of Binomial-related matrices have been introduced. Such matrices are circulant matrices whose the first row is the coefficients of (x+zy)n, where z is a complex number of norm 1 and n is a positive integer. In the case where z∈ \1,-1,i,-i\, the explicit formula for the determinant of such matrices are completely determined. Known results on the determinants of binomial circulant matrices can be viewed as special cases. Finally, some open problems are discussed.