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https://cs.uwaterloo.ca/twiki/pub/TWiki/TWikiLogos/uwlogo_long.pngImportantOpenProblems
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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... (last changed by JeffreyShallit)2018-02-28T11:08:44ZJeffreyShallitEqualityLanguages
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.displaymath { font style:italic; padding:20px; border:dotted 1px #cccccc; } .rm { font style:normal; } .references { font style:italic; } Equality Languages The... (last changed by JeffreyShallit)2018-02-28T11:06:22ZJeffreyShallitExponentofMorphism
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Let w be an infinite word generated (by iteration) by a given morphism. Let p be any rational number. If there exists a word u such that up is a factor of... (last changed by JeffreyShallit)2018-02-22T13:31:09ZJeffreyShallitLocalGlobal
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Is there a positive integer n 2 and words u1, u2, ..., un such that both equalities (u1u2 un)2 u12u22 un2, (u1u2 un)3 u13u23 un3 hold simultaneously... (last changed by JeffreyShallit)2018-02-22T13:25:48ZJeffreyShallitFraenkelsProblem
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Fraenkel`s problem: A word is balanced if the number of occurrences of any letter in any two factors of equal length differ at most by 1. Given a k letter alphabet... (last changed by JeffreyShallit)2018-02-22T09:44:55ZJeffreyShallitSubwordComplexity
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The subword complexity of an infinite word w is the function that sends each non negative integer n to the number of distinct factors of length n . Note: this... (last changed by JeffreyShallit)2018-02-22T09:31:01ZJeffreyShallitIsPiNormal
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Is Pi; Normal? A real number x is normal to base b if all finite words w over the alphabet {0,1, ..., b 1} occur as factors of the base b expansion of x with... (last changed by JeffreyShallit)2018-02-22T09:30:00ZJeffreyShallitPrimitiveWordsContextFree
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A finite word w is primitive if it is not a nontrivial power of another word, that is, if w uk for k 1 implies that k 1. Is the set of all primitive... (last changed by JeffreyShallit)2018-02-22T09:12:10ZJeffreyShallitNivatConjecture
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Nivat`s conjecture: Consider 2 dimensional words, that is, sets of letters indexed by Z2. Is the following conjecture true? If the number of distinct m ... (last changed by JeffreyShallit)2018-02-22T09:09:10ZJeffreyShallitHHPVProblem
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The Brown Freedman Halbeisen Hungerb... (last changed by JeffreyShallit)2018-02-22T09:02:00ZJeffreyShallitWordkAvoidable
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Is a given word k avoidable? A word x is called k avoidable if there exists an infinite word w over a k letter alphabet such that no morphic image of x occurs... (last changed by JeffreyShallit)2018-02-22T08:56:28ZJeffreyShallitCodeUniquePrimitiveRoot
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Does every code have a unique primitive root? A set of words L is a code if every word has at most one factorization over L . For two languages L and R of words... (last changed by JeffreyShallit)2018-02-22T08:55:14ZJeffreyShallitSquarefreeWordEnumeration
https://cs.uwaterloo.ca/twiki/view/CoWiki/SquarefreeWordEnumeration
What is the number of square free words? A word has a square if it contains two consecutive occurrences of the same factor. For an alphabet of size k 3, we ask for... (last changed by JeffreyShallit)2018-02-22T08:49:54ZJeffreyShallitWebSearch
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(last changed by TWikiContributor)2015-05-15T21:32:24ZTWikiContributorWebSearchAdvanced
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(last changed by TWikiContributor)2015-05-15T21:32:20ZTWikiContributorKolakoskiFrequencies
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The Kolakoski word can be defined in a number of different ways, but probably the simplest is as the unique infinite word k over the alphabet {1, 2}, starting with... (last changed by JeffreyShallit)2014-02-13T20:51:55ZJeffreyShallit