Lucas Sayı Dizisinin Bilgi Entropisi Yönünden İncelenmesi

Lucas sayı dizisi, ilk iki terimi L_1=1 ve L_2=3 olmak üzere L_n=L_(n-1)+L_(n-2) indirgeme bağıntısı ile elde edilir. Bu çalışmada Lucas sayı dizisi, bilgi entropisi yönünden incelendi. Sistemlerin entropi değerleri hesaplanırken sayı üçgenlerinden yararlanmak olağan bir uygulamadır. Fibonacci sayıları Pascal üçgeninden ve Lucas sayıları Lucas üçgeninden elde edilebileceğinden, bu üçgenlerin entropisi hesaplandı. Elde edilen sonuçlar Leibniz’in harmonik üçgeniyle kıyaslandı.

Anahtar Kelimeler:

Entropi, Lucas Sayı Dizisi, Pascal Üçgeni, Lucas Üçgeni, Leibniz Üçgeni

Investigation of Lucas Number Sequence in Term of Information Entropy

Lucas number sequence is obtained by the recurrence relation L_n=L_(n-1)+L_(n-2)with initial terms L_1=1 and L_2=3. In this paper, the Lucas number sequence was investigated in term of information entropy. The using of number triangles is an always application when the entropy measures of systems are calculated. Since the Fibonacci number sequence can be obtained from Pascal triangle and the Lucas number sequence can be obtained from Lucas triangle, the entropy measures of these triangles were calculated. The obtained results were compared with the harmonic triangle of Leibniz.

Keywords:

Entropy, Lucas Number Sequence, Pascal Triangle, Lucas Triangle, Leibniz Triangle,

PDF

___

I. D. Stones, “The Harmonic Triangle: Opportunities for Pattern Identification and Generalization,” Math. Teach., vol. 76, no. 5, 2021.
C. Tsallis, M. Gell-Mann, and Y. Sato, “Asymptotically scale-invariant occupancy of phase space makes the entropy Sq extensive,” Proc. Natl. Acad. Sci., vol. 102, no. 43, pp. 15377–15382, Oct. 2005
X. Gao and Y. Deng, “The Pseudo-Pascal Triangle of Maximum Deng Entropy,” Int. J. Comput. Commun. Control, vol. 15, no. 1, Feb. 2020.
Y. Song and Y. Deng, “Entropic Explanation of Power Set,” Int. J. Comput. Commun. Control, vol. 16, no. 4, Aug. 2021.
S. R. Nurshiami, A. Wardayani, and K. H. Setiani, “Karakteristik Segitiga Lucas,” J. Ilm. Mat. dan Pendidik. Mat., vol. 11, no. 1, p. 11, May 2020.
N. Robbins, “The lucas triangle revisited,” Fibonacci Q., vol. 43, no. 2, 2005.
R. Sivaraman, “On Some Properties of Leibniz’s Triangle,” Math. Stat., vol. 9, no. 3, pp. 209–217, May 2021.
İ. Tuğal, B. Şahin, A. Şahin, “The Shannon Entropy of Fibonacci Numbers”, MATI vol. 4, no 1, pp. 12-22, Jan. 2022.