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J. R. Jachymski, Schroder, Bernd; Stein, D., James Jr., “A connection between fixed-point theorems and tiling problems,” Journal of Combinatorial Theory, Series A, Vol. 87, No. 2, 1999, pp. 273-286. doi:10.1006/jcta.1998.2960

has been cited by the following article:

• TITLE: A Tiling Lemma and Its Application to the Ratio Test for Convergence of Series

  AUTHORS: James D. Stein Jr., Linda Ho

  KEYWORDS: Tiling, Ratio Test, Banach Fixed-Point Theorem

  JOURNAL NAME: Advances in Pure Mathematics, Vol.1 No.5, September 21, 2011

  ABSTRACT: We prove that any collection which tiles the positive integers must contain one of two types of sub-collections. We then use this result to prove a variation of the Ratio Test for convergence of series. This version of the Ratio Test shows the convergence of certain series for which the Root Test (which is known to be more powerful than the conventional Ratio Test) fails. This version of the Ratio Test is also used to prove a version of the Banach Contraction Principle for self-maps of a complete metric space.