Combinatorics of Dyadic Intervals: Consistent Colorings
Anna Kamont, Paul F.X. Muller
TL;DR
This paper investigates the conditions under which consistent and homogeneous colorings of increasing families of dyadic intervals can be achieved, providing a comprehensive analysis of solvability.
Contribution
It characterizes the precise conditions for the existence of such colorings, advancing understanding in combinatorics of dyadic intervals.
Findings
Identifies when the coloring problem is solvable.
Provides necessary and sufficient conditions for consistent colorings.
Clarifies limitations and possibilities in dyadic interval colorings.
Abstract
We study the problem of consistent and homogeneous colourings for increasing families of dyadic intervals. We determine when this problem can be solved and when not.
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Taxonomy
TopicsLimits and Structures in Graph Theory · semigroups and automata theory · Mathematical Dynamics and Fractals