A connection between fixed-point theorems and tiling problems (Q1304626)

This paper mainly studies generalizations of the Banach contraction principle which states that any contraction on a complete metric space has a unique fixed point. A method for attacking such problems by considering a related problem on tiling the integers is developed. This technique simultaneously automates many of the unwieldy arguments, and makes for more visual proofs. The authors hope that presenting this combinatorial approach will serve a dual purpose: to stimulate the investigation of other analytical problems through combinatorics, and also to generate an interesting class of combinatorial problems.