A Resolution of the McCarty Conjecture

Abstract

The McCarty Conjecture states that any McCarty Matrix (an $n\times n$ matrix $A$ with positive integer entries and each of the $2n$ row and column sums equal to $n$), can be additively decomposed into two other matrices, $B$ and $C$, such that $B$ has row and column sumsets both equal to $\{1,2,...n\}$, and $C$ has row and column sumsets both equal to $\{0,1,...n-1\}$. The problem can also be formulated in terms of bipartite graphs. In this paper we use probabilistic methods to resolve this conjecture.

There appears to be an error in the proof of the main result