Computation of k-ary Lyndon Words Using Generating Functions and Their Differential Equations
FILOMAT, cilt.32, sa.10, ss.3455-3463, 2018 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 32 Sayı: 10
- Basım Tarihi: 2018
- Doi Numarası: 10.2298/fil1810455k
- Dergi Adı: FILOMAT
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.3455-3463
- Anahtar Kelimeler: Lyndon words, Generating functions, Ordinary differential equations, Apostol-Bernoulli numbers and polynomials, Stirling numbers, Algorithm, EULER POLYNOMIALS, Q-EXTENSIONS, BERNOULLI, NECKLACES, BEADS
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Akdeniz Üniversitesi Adresli: Evet
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.