Ryser's Conjecture and Stochastic matrices

TL;DR

This paper proves that circulant Hadamard matrices can only exist of order 4, using a novel approach involving stochastic matrices, thereby confirming the limited number of such matrices.

Contribution

It introduces a new method linking circulant Hadamard matrices to stochastic matrices to establish their non-existence for orders other than 4.

Findings

Proves that circulant Hadamard matrices only exist of order 4.

Establishes that there are exactly 10 circulant Hadamard matrices.

Provides a new proof technique connecting stochastic matrices and Hadamard matrices.

Abstract

Assume that $H$ is a circulant Hadamard matrix of order $n\geq 4$. We consider an appropriate stochastic matrix $S$ of order $n$ depending on $H$. This allows us to prove that $n = 4$. Thus, there are only $10$ circulant Hadamard matrices.