Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.

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How to determine if there exists a non-zero vector in the kernel

If you are given a $0$-$1$ circulant matrix with $n$ rows and $n$ columns, is there an efficient way of determining if there exists a non-zero $\{-1,0,1\}$-vector in its kernel? Could this problem ...