The Littlewood-Offord problem concerns the number of subsums of a set of vectors that fall in a given convex set. We present a discrete variation of the Littlewood-Offord problem where we estimate the number of subsums that are $(0,1)$-vectors. We then utilize this to find the maximum order of graphs with given rank or corank. The rank of a graph G is the rank of its adjacency matrix $A(G)$ and the corank of G is the rank of $A(G)+I$.
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Esmailian et al. (2024) studied this question.
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