ImportantOpenProblems < CoWiki

---+++ Important Open Problems

At the Oberwolfach meeting on Combinatorics on Words in 2010, the participants suggested a list of 18 important open problems in the field. In February 2018, it was updated to include some recent progress on these problems.

Here is the list:

1. [[IsPiNormal?][Is &Pi; Normal?]]

2. [[KolakoskiFrequencies][Frequencies in the Kolakoski word]]

3. [[WordEquationSatisfiability][Word Equation Satisfiability]]

4. [[LargestIndependentSystem][Largest Independent System of Word Equations]]

5. [[FraenkelsProblem][Fraenkel's Problem]]

6. [[BrzozowskiConjecture][Brzozowski's Conjecture]]

7. [[SquarefreeWordEnumeration][Enumeration of Squarefree Words]]

8. [[WordkAvoidable][Does there exist a k-avoidable word?]]

9. [[PrimitiveWordsContextFree][Is the language of primitive words context-free?]]

10. [[PCP3Decidable][Is PCP(3) Decidable?]]

11. [[NivatConjecture][Nivat's Conjecture]]

12. [[ReconstructionfromSubwords][Reconstruction from subwords]]

13. [[HHPVProblem][The Brown-Freedman-Halbeisen-Hungerbühler-Pirillo-Varricchio Problem]]

14. [[SAdicConjecture][The S-adic conjectures]]

15. [[CodeUniquePrimitiveRoot][Do Codes have unique primitive roots?]]

16. [[ExponentofMorphism][Is the exponent of a morphism computable?]]

17. [[MatricesGenerateFreeGroup][Can we decide if a set of matrices generates the free group?]]

18. [[NumberofRightSpecialFactors][The number of right special factors]]

-- Main.JeffreyShallit - 13 Oct 2010
This topic: CoWiki > WebHome > ImportantOpenProblems
Topic revision: r5 - 2018-02-28 - JeffreyShallit