Abelian Patterns in Partial Words

F. Blanchet-Sadri       Ian Coley       Benjamin De Winkle

Abstract
Implementation
Paper

   Use the below applet to calculate the hole density of either a finite word or a fixed point of a given morphism.
   The morphism calculation will work with any number of letters greater than or equal to two, but the calculations will run slowly for larger alphabets. To achieve a fixed point, your 'a' morphism must start with an 'a'. Finally, be sure that your morphisms have at least two letters, otherwise the fixed point will not grow.
   The finite word calculation can take any number of lowercase letters (a-z). However, the word does not need to include consecutive letters of the alphabet, e.g. 'acbcabe' would be allowed.
   The applet output is in terms of subword length to allow for more data. For example, if your abelian power is p, subwords of length 4 correspond to strings of length 4p in your fixed point. For finite words, all possible subword lengths will be calculated. For fixed points, subword lengths up to length 100 will be calculated (corresponding to strings of length 100*p).

To run this program, all you will need is the latest java plug-in.

Keywords:      Combinatorics on Words; Partial Words; Abelian Powers; Abelian Patterns.

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Acknowledgement: This material is based upon work supported by the National Science Foundation under Grant No. DMS-1060775.
Disclaimer: Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.
Funded by the NSF.
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