TWiki's CoWiki webThe CoWiki web of TWiki. TWiki is a Web-Based Collaboration Platform for the Enterprise.https://cs.uwaterloo.ca/twiki/view/CoWikiCopyright 2023 by contributing authors2023-06-07T17:32:35ZWebStatisticshttps://cs.uwaterloo.ca/twiki/view/CoWiki/WebStatistics2023-06-07T17:32:35ZStatistics for CoWiki Web Month: Topic views: Topic saves: File uploads: Most popular topic views: Top contributors for topic save... (last changed by TWikiAdminGroup)TWikiAdminGroupImportantOpenProblemshttps://cs.uwaterloo.ca/twiki/view/CoWiki/ImportantOpenProblems2018-02-28T11:08:44ZImportant 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)JeffreyShallitEqualityLanguageshttps://cs.uwaterloo.ca/twiki/view/CoWiki/EqualityLanguages2018-02-28T11:06:22Z.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)JeffreyShallitExponentofMorphismhttps://cs.uwaterloo.ca/twiki/view/CoWiki/ExponentofMorphism2018-02-22T13:31:09ZLet 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)JeffreyShallitLocalGlobalhttps://cs.uwaterloo.ca/twiki/view/CoWiki/LocalGlobal2018-02-22T13:25:48ZIs 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)JeffreyShallitFraenkelsProblemhttps://cs.uwaterloo.ca/twiki/view/CoWiki/FraenkelsProblem2018-02-22T09:44:55ZFraenkel`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)JeffreyShallitSubwordComplexityhttps://cs.uwaterloo.ca/twiki/view/CoWiki/SubwordComplexity2018-02-22T09:31:01ZThe 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)JeffreyShallitIsPiNormalhttps://cs.uwaterloo.ca/twiki/view/CoWiki/IsPiNormal2018-02-22T09:30:00ZIs 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)JeffreyShallitPrimitiveWordsContextFreehttps://cs.uwaterloo.ca/twiki/view/CoWiki/PrimitiveWordsContextFree2018-02-22T09:12:10ZA 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)JeffreyShallitNivatConjecturehttps://cs.uwaterloo.ca/twiki/view/CoWiki/NivatConjecture2018-02-22T09:09:10ZNivat`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)JeffreyShallitHHPVProblemhttps://cs.uwaterloo.ca/twiki/view/CoWiki/HHPVProblem2018-02-22T09:02:00ZThe Brown Freedman Halbeisen Hungerb... (last changed by JeffreyShallit)JeffreyShallitWordkAvoidablehttps://cs.uwaterloo.ca/twiki/view/CoWiki/WordkAvoidable2018-02-22T08:56:28ZIs 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)JeffreyShallitCodeUniquePrimitiveRoothttps://cs.uwaterloo.ca/twiki/view/CoWiki/CodeUniquePrimitiveRoot2018-02-22T08:55:14ZDoes 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)JeffreyShallitSquarefreeWordEnumerationhttps://cs.uwaterloo.ca/twiki/view/CoWiki/SquarefreeWordEnumeration2018-02-22T08:49:54ZWhat 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)JeffreyShallitWebSearchhttps://cs.uwaterloo.ca/twiki/view/CoWiki/WebSearch2015-05-15T21:32:24Z (last changed by TWikiContributor)TWikiContributorWebSearchAdvancedhttps://cs.uwaterloo.ca/twiki/view/CoWiki/WebSearchAdvanced2015-05-15T21:32:20Z (last changed by TWikiContributor)TWikiContributor