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Dona Strauss works on algebraic methods in Ramsey theory. Her joint paper with Neil Hindman and Imre Leader examines when different Milliken-Taylor systems can be monochromatic together.^[ref]

Compression removes zero entries and repeated consecutive coefficients. For positive coefficient patterns, the resulting sequences must satisfy a positive-rational-proportionality criterion in the theorem's simultaneous setting. The result exposes structure behind a coloring problem whose individual patterns already satisfy strong partition properties.^[ref]

Imre Leader studies extremal combinatorics and Ramsey theory. His Cambridge research profile identifies these areas.^[ref]

With Neil Hindman and Dona Strauss, he studied compatibility between Milliken-Taylor systems. The coefficients of two systems cannot be chosen arbitrarily if both are to be monochromatic in the required simultaneous sense. Their theorem identifies a positive-rational-proportionality condition for compressed positive coefficient patterns, sharpening the distinction between individually unavoidable patterns and jointly compatible ones.^[ref]

Neil Hindman works on Ramsey theory and algebraic methods for finding structured monochromatic sets. With Vitaly Bergelson and Kendall Williams, he developed polynomial extensions of the Milliken–Taylor theorem, using ultrafilters and their algebra.^[ref]

With Imre Leader and Dona Strauss, he also studied when different Milliken-Taylor systems can be monochromatic simultaneously. The coefficient patterns impose genuine compatibility conditions.^[ref]

By Neil Hindman, Imre Leader and Dona Strauss. Proceedings of the Edinburgh Mathematical Society46,45–61. DOI: doi.org/10.1017/S001309150200010X

Author-hosted final manuscript: nhindman.us/research/separate.pdf

Definition1.5 and Theorem1.7 give compression and the positive-rational-proportionality criterion for simultaneously monochromatic positive-coefficient systems.