INTERPRETASI KOMBINATORIAL BILANGAN EULER

Authors

  • Rektor Sianturi Universitas Sumatera Utara

DOI:

https://doi.org/10.46244/visipena.v6i1.359

Keywords:

Bilangan Euler, Kombinatorial, Permutasi

Abstract

Kombinatorial bilangan Euler ialah suatu proses yang menghitung banyaknya alternatif permutasi dari himpunan bilangan dengan jumlah genap. Interpretasi kombinatorial bilangan Euler membutuhkan pemahaman dasar mengenai penurunan (descent) dan kenaikan (ascent) dalam permutasi. Beberapa artikel dan buku membahas tentang bilangan Euler, kombinatorial bilangan Euler, barisan bilangan Euler, bentuk umum bilangan Euler dengan berbagai metode. Dalam penelitian ini akan membahas lebih lanjut bagaimana bentuk umum interpretasi kombinatorial bilangan Euler yang didefinisikan pada progres aritmatika umum {a, a + d, a + 2d, …} kemudian membentuk algoritmanya.

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References

Bona, M, 2004, Combinatorics of Permutations.Discrete Mathematics and its Applications. Boca Raton : Chapman & Hall/CRC.

Carlitz, L. 1954. Q-bernoulli and Eulerian Numbers. Transaction of the American Mathematical Society, 76: 332-350.

Carlitz, L. 1975. A Combination Property of q-Eulerian Numbers. The American Mathematical Monthly, 82:51-54

Khattri, S.K., Witkowski, A. 2012. Euler’s Number and Some Means*. Tamsui Oxford Journal of Information and Mathematical Sciences, 28(4) : 369-377

Riordan, J. 1958. An Introduction of Combinatorial Analysis. Wiley Publication in Mathematical Statistics. New York : John Wiley & Sons.

Stanley, R.P. 1996. Enumerative Combinatorics, vol 1. Of Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge, UK.

Xiong, T. Tsao, H.P. and Hall, J.I. 2013, General Eulerian Numbers and Eulerian Polynomials, Journal of Mathematics, Article ID 629132, 9 pages.

Xiong, T. Tsao, H.P and Hall, J.I. 2014. Combinatorial Interpretation of General Eulerian Numbers, Journal of Discrete Mathematics, Article ID 870596, 6 pages.

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Published

2015-06-30

How to Cite

Rektor Sianturi. (2015). INTERPRETASI KOMBINATORIAL BILANGAN EULER. Visipena, 6(1), 102–110. https://doi.org/10.46244/visipena.v6i1.359

Issue

Vol. 6 No. 1 (2015)

Section

Articles

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