Küçükoğlu, İremŞimşek, Yılmaz2021-02-192021-02-1920180354-5180https://doi.org/10.2298/FIL1810455Khttps://hdl.handle.net/20.500.12868/511KUCUKOGLU, IREM/0000-0001-9100-2252By using generating functions technique, we investigate some properties of the k-ary Lyndon words. We give an explicit formula for the generating functions including not only combinatorial sums, but also hypergeometric function. We also derive higher-order differential equations and some formulas related to the k-ary Lyndon words. By applying these equations and formulas, we also derive some novel identities including the Stirling numbers of the second kind, the Apostol-Bernoulli numbers and combinatorial sums. Moreover, in order to compute numerical values of the higher-order derivative for the generating functions enumerating k-ary Lyndon words with prime number length, we construct an efficient algorithm. By applying this algorithm, we give some numerical values for these derivative equations for selected different prime numbers.eninfo:eu-repo/semantics/openAccessLyndon wordsGenerating functionsOrdinary differential equationsApostol-Bernoulli numbers and polynomialsStirling numbersAlgorithmArticle10.2298/FIL1810455K321034553463Q3WOS:000461181400006N/A