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Partition Theorems for Spaces of Variable Words
Author(s) -
Bergelson Vitaly,
Blass Andreas,
Hindman Neil
Publication year - 1994
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/s3-68.3.449
Subject(s) - mathematics , partition (number theory) , generalization , linear subspace , ramsey theory , metric space , variable (mathematics) , discrete mathematics , pure mathematics , combinatorics , mathematical analysis
Furstenberg and Katznelson applied methods of topological dynamics to Ramsey theory, obtaining a density version of the Hales–Jewett partition theorem. Inspired by their methods, but using spaces of ultrafilters instead of their metric spaces, we prove a generalization of a theorem of Carlson about variable words. We extend this result to partitions of finite or infinite sequences of variable words, and we apply these extensions to strengthen a partition theorem of Furstenberg and Katznelson about combinatorial subspaces of the set of words.