A Discrete Variation of the Littlewood-Offord Problem

Hossein  Esmailian; Ebrahim Ghorbani

doi:10.37236/11956

Hossein Esmailian
Ebrahim Ghorbani

DOI: https://doi.org/10.37236/11956

Abstract

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 $A(G)+I$.