Computation of k-ary Lyndon words using generating functions and their differential equations
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Tarih
2018
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Univ Nis, Fac Sci Math
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
By 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.
Açıklama
KUCUKOGLU, IREM/0000-0001-9100-2252
Anahtar Kelimeler
Lyndon words, Generating functions, Ordinary differential equations, Apostol-Bernoulli numbers and polynomials, Stirling numbers, Algorithm
Kaynak
Filomat
WoS Q Değeri
N/A
Scopus Q Değeri
Q3
Cilt
32
Sayı
10
