# Diagonal sum of infinite image partition regular matrices

@article{Patra2017DiagonalSO, title={Diagonal sum of infinite image partition regular matrices}, author={Sourav Patra and Ananya Shyamal}, journal={arXiv: Combinatorics}, year={2017} }

A finite or infinite matrix $A$ is image partition regular provided that whenever $\mathbb N$ is finitely colored, there must be some $\vec{x}$ with entries from $\mathbb N$ such that all entries of $A\vec{x}$ are in some color class. In [6], it was proved that the diagonal sum of a finite and an infinite image partition regular matrix is also image partition regular. It was also shown there that centrally image partition regular matrices are closed under diagonal sum. Using Theorem 3.3 of [2…

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