On the singularity of random combinatorial matrices

Mathematics – Combinatorics

Scientific paper

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16 pages

Scientific paper

It is shown that a random $(0,1)$ matrix whose rows are independent random
vectors of exactly $n/2$ zero components is non-singular with probability
$1-O(n^{-C})$ for any $C>0$. The proof uses a non-standard inverse-type
Littlewood-Offord result.

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