Circulants form a well-studied and important class of matrices, and they arise in many algebraic and combinatorial contexts, in particular as multiplication tables of cyclic groups and as special classes of latin squares. There is also a known connection between circulants and mathematical juggling. The purpose of this note is to expound on this connection developing further some of its properties. We also formulate some problems and conjectures with some computational data supporting them.
R. A. Brualdi and M. W. Schroeder, Circulant matrices and mathematical juggling, The Art of Discrete and Applied Mathematics 1 (2018), 1-17.