On circulant thin Lehman matrices

The class of Lehman matrices is a key structure of characterization of minimally non-ideal clutters. The notion of -overlapped factorizations of cyclic groups produces an infinite family of circulant thin Lehman matrices. In this paper, we prove essential properties of the -overlapped factorizations of cyclic groups and completely determine the shapes of circulant thin Lehman matrices with small constant line sum, which solves the ideal counterpart of the so-called Grinstead's conjecture for the circulant partitionable graphs in this case.