Words, tilings and combinatorial spectra

Abstract

We will introduce some combinatorics for given words. Such combinatorics can essentially determine the exact information of letters as well as the patterns of words. This method can induce a characterization of the so-called local indistinguishability for one dimensional tilings, which allows us to have a new development for tiling bialgebras. Using those combinatorics associated with words and one dimensional tilings, we can obtain their combinatorial spectra as certain sets of functions or positive real numbers. We will also discuss higher dimensional tilings. Furthermore, we will try to compute some genome examples.