Language and tilings

This page gathers ideas for refactorization of sage.combinat.words and a creation of a class for tilings. A word (in the way they are considered in Sage) should be considered as particular case of tilings. The two main notions which coexist with some generality are : tiling generated by local rules (subshift of finite type) and tiling generated by substitution rule (morphic word, adic systems, ...).

generic definition : A tiling is a map from an enumerated set to an alphabet. A finite word is a word for which the enumeration set is an interval of integers (?), an infinite word ? a bi-infinite word ?

Structure

Tiling space

The highest level class should be something like TilingSpace. It contains an enumerated set, an alphabet (and optionally a way of plotting). Do we always assume that the enumerated set is either a group (like ZZ) or a sub-semigroup of a group (like NN) ?

Tiling and words

Factor, equality

By going from ZZ to ZZ^2 or more general groups, the notion of factor is not well defined. It depends of some shape. In ZZ we take integers interval

Substitutive and adic languages

• Equality for purely morphic words is decidable (J. Honkala, CANT, chapter 10)