Welcome to the Pattern Avoidance Automated Archive! Please input a pattern over any alphabet of variables below, and the Archive will attempt to determine the avoidability index or bounds of it, using the algorithms described in our paper. This may take a great deal of time. To verify suggested HDOLs, please visit the HDOL verification algorithm located here .
To use, just input a pattern over any set of variables (for example ABABA) in the box and press investigate. The Pattern Avoidance Automated Archive will first check for unavoidability. This stage of testing can be quite sluggish for patterns with very large numbers of different variables. If no reason to suspect unavoidability is found, it will attempt to generate HDOLs which avoid it. Note that the HD0L finder is not implemented for patterns with more than three distinct variables, and even then, may take a
VERY LONG TIME
Pressing "Stop It" while the HD0L finder is running will allow you to enter a different pattern to investigate.
HD0LS are output with "$$$$" between images of letters under the outer morphism, and "****" between images of letters under the inner morphism, and we will use "^" to represent a hole. For example "aab^$$$$bbab?abb****ba" would translate to the HDOL f(a) = abb, f(b)=ba,g(a)=aab^, and g(b)=bbab.