2019/12/18 by Mohammad Golshani, Saharon Shelah, Golshani, Mohammad +1
Computer Science · Mathematics · #Advanced Topology and Set Theory #Combinatorics #Complexity and Algorithms in Graphs #Discrete mathematics #Graph #Iterated function #Lambda #Limits and Structures in Graph Theory #Linear subspace #Mathematical analysis #Mathematics #Modulo #Natural number #Partition (number theory) #Physics #Pure mathematics #Quantum mechanics #Ramsey theory #Ramsey's theorem #Subspace topology #math.CO
paper · pdf · doi:10.48550/arxiv.1912.08643
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2019/12/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Consider the Hales-Jewett theorem. The k-dimensional version of it tells us that the combinatorial space UM, Λ = \ η| η: M → Λ\ has, under suitable assumptions, monochromatic k-dimensional subspaces, where by a k-dimensional subspace we mean there exist a partition ⟨ N0, N1, ⋯, Nk ⟩ of M such that N1, ⋯, Nk ≠ ∅ (but we allow N0 to be empty) and some ρ0: N0 → Λ, such that the subspace consists of those ρ∈ UM, Λ such that for 0