Permutations of ℤ^d with restricted movement

2015/10/05 by Schmidt, Klaus, Strasser, Gabriel
#37A35 #37B10 #37B50 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1510.01068

Abstract

We investigate dynamical properties of the set of permutations of ℤ^d with restricted movement, i.e., permutations π of ℤ^d such that π(n)-n lies, for every n∈ ℤ^d, in a prescribed finite set A⊂ ℤ^d. For d=1, such permutations occur, for example, in restricted orbit equivalence, or in the calculation of determinants of certain bi-infinite multi-diagonal matrices. For d≥2 these sets of permutations provide natural classes of examples of multidimensional shifts of finite type.

Related

• Permutations with restricted movement
• Master's thesis: Permutations With Restricted Movement
• Permutations and beta-shifts
• Forbidden patterns and shift systems
• An upper bound on the number of high-dimensional permutations