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By Vitaly Bergelson.

Published in Ergodic Theory of Z-d-actions, London Mathematical Society Lecture Note Series 228, pp. 1–61.

Author-hosted text: people.math.osu.edu/bergelson.1/ertupdatenov6.pdf

Publication details: Author's publication list, first entry

Kendall Williams coauthored work on polynomial extensions of the Milliken–Taylor theorem with Vitaly Bergelson and Neil Hindman. The primary manuscript verifies this exact byline.^[ref]

Their results find monochromatic polynomial configurations built from separated finite blocks of a sequence. The approach combines Ramsey theory with the algebra of ultrafilters, extending structured finite-sum patterns to more general polynomial images.^[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 Vitaly Bergelson, Neil Hindman and Kendall Williams. Author-hosted primary manuscript: people.math.osu.edu/bergelson.1/BHW_PolynomialMT.pdf

Definition1.5 and Theorem1.6 specify the positive-coefficient separated-block systems and their monochromatic sum subsystems; Theorem1.4 states the underlying Milliken-Taylor theorem.

Vitaly Bergelson studies the interaction of ergodic theory with Ramsey theory and arithmetic patterns. His Ohio State publication list documents work on recurrence, polynomial configurations and semigroup actions.^[ref]

His Ergodic Ramsey Theory - an update by Vitaly Bergelson develops the exchange between recurrence in dynamical systems and structured configurations in subsets of integers. With Neil Hindman and Kendall Williams, he also extended Milliken–Taylor theorem patterns to polynomial settings, using algebraic properties of ultrafilters to obtain monochromatic configurations.^[ref][ref]