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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 저널정보
- 장전수학회 Advanced Studies in Contemporary Mathematics Advanced Studies in Contemporary Mathematics Vol.30 No.4
- 발행연도
- 2020.1
- 수록면
- 529 - 538 (10page)
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The main aim of this paper is to nd out some relationships between the numbers of Lyndon words and a certain class of combinatorial numbers which contains nite sums of powers of binomial coe cients and whose generating functions were constructed and investigated by Simsek in \Generating functions for nite sums involving higher powers of binomial coe cients: Analysis of hypergeometric functions including new families of polynomials and numbers, J. Math. Anal. Appl. 477 (2019), 1328{1352". By applying not only the Dirichlet convolution formula, but also the Mobius inversion formula, we obtain some identities containing the Mobius function, the Euler's totient function, the numbers of Lyndon words, the numbers of necklaces, the Stirling numbers of the second kind, and the aforementioned class of combinatorial numbers. Moreover, a few special cases and consequences of our results are considered. In particular, it should be noted here that in the special case when we take the power of the binomial coe cients to be 1, some of our results are reduced to several results obtained by Kucukoglu and Simsek in \Identities and Derivative Formulas for the Combinatorial and Apostol-Euler Type Numbers by Their Generating Functions, Filomat 32(20) (2018), 6879{6891".
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참고문헌 (32)
참고문헌 신청
T. M. Apostol / 1976 / Introduction to Analytic Number Theory / Springer-Verlag
J. Berstel / 2007 / The origins of combinatorics on words / European J. Combin 28:996~1022
M. Bona / 2007 / Introduction to Enumerative Combinatorics / The McGraw-Hill Companies Inc
K. N. Boyadzhiev / Binomial transform and the backward difference
N. P. Cakic / 2004 / On generalized Stirling numbers and polynomials / Mathematica Balkanica 18:241~248
J. Berstel / 2007 / The origins of combinatorics on words / European J. Combin 28:996~1022
M. Bona / 2007 / Introduction to Enumerative Combinatorics / The McGraw-Hill Companies Inc
K. N. Boyadzhiev / Binomial transform and the backward difference
N. P. Cakic / 2004 / On generalized Stirling numbers and polynomials / Mathematica Balkanica 18:241~248
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