Blog
About

7
views
0
recommends
+1 Recommend
0 collections
    0
    shares
      • Record: found
      • Abstract: found
      • Article: found
      Is Open Access

      Revisiting the Nilpotent Polynomial Hales-Jewett Theorem

      Preprint

      ,

      Read this article at

      Bookmark
          There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

          Abstract

          Answering a question posed by Bergelson and Leibman in [7], we establish a nilpotent version of the Polynomial Hales-Jewett Theorem that is a common generalization of both the main theorem in [7] and the Polynomial Hales-Jewett Theorem (PHJ). Important to the formulation and the proof of our main theorem is Shuungula's, Zelenyuk's, and Zelenyuk's [30] notion of a relative syndetic set (relative with respect to two closed non-empty subsets of \(\beta G\)). Using their language we first reformulate the classical PHJ as a theorem about abelian groups before we proceed to generalize it to nilpotent groups. As a corollary of our main theorem we prove an extension of the restricted van der Waerden Theorem to nilpotent groups, which involves nilprogressions. We also offer a reformulation of the Density Hales-Jewett Theorem based on an extension of the notion of relative syndeticity to a relative version of upper and lower Banach density.

          Related collections

          Most cited references 13

          • Record: found
          • Abstract: not found
          • Article: not found

          The structure of approximate groups

            Bookmark
            • Record: found
            • Abstract: not found
            • Article: not found

            An ergodic Szemerédi theorem for IP-systems and combinatorial theory

              Bookmark
              • Record: found
              • Abstract: not found
              • Article: not found

              Topological dynamics and combinatorial number theory

                Bookmark

                Author and article information

                Journal
                2016-07-18
                Article
                1607.05320

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                Custom metadata
                math.CO

                Combinatorics

                Comments

                Comment on this article