Factorizations of the Pascal matrix via a generalized second order recurrent matrix

TATAR, G.; KILIÇ, E.; ULUTAŞ, Y. T.; ÖMÜR, N.

Factorizations of the Pascal matrix via a generalized second order recurrent matrix

E. KILIÇ, (TOBB Ekonomi ve Teknoloji Üniversitesi, Ankara, Türkiye)

N. ÖMÜR, (Kocaeli Üniversitesi, Kocaeli, Türkiye)

G. TATAR, (Kocaeli Üniversitesi, Kocaeli, Türkiye)

Y. T. ULUTAŞ (Kocaeli Üniversitesi, Kocaeli, Türkiye)

Hacettepe Journal of Mathematics and Statistics

1 0

Yıl: 2009 Cilt: 38 Sayı: 3 Sayfa Aralığı: 305 - 316 Metin Dili: İngilizce İndeks Tarihi: 29-07-2022

Factorizations of the Pascal matrix via a generalized second order recurrent matrix

Öz:

In this paper, we consider positively and negatively subscripted terms of a generalized binary sequence {$U_n$} with indices in arithmetic pro- gression. We give a factorization of the Pascal matrix by a matrix associated with the sequence {$U_{pmkn$} for a fixed positive integer k, gen- eralizing results of Kılı¸c and Tascı; Lee, Kim and Lee; Stanica; and Zhizheng and Wang. Some new factorizations and combinatorial iden- tities are derived as applications. Therefore we generalize the earlier results on the factorizations of the Pascal matrix.

Anahtar Kelime:

Konular: Matematik İstatistik ve Olasılık

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık

[1] Cheon, G. S. and Kim, J. S. Stirling matrix via Pascal matrix, Linear Algebra Appl. 329, 49–59, 2001.
[2] Kilic, E. and Stanica, P. Factorizations and representations of second linear recurrences with incides in aritmetic progressions, Bol. Soc. Mat. Mexicana (in press).
[3] Kilic, E. and Tasci, D. The linear algebra of the Pell matrix, Bol. Soc. Mat. Mexicana 2 (11), 163–174, 2005.
[4] Lawden, G.H. Pascal matrices, Mathematical Gazette 56 (398), 325–327, 1972.
[5] Lee, G.Y., Kim, J. S. and Lee, S.G. Factorizations and eigenvalues of Fibonacci and symmetric Fibonacci matrices, Fibonacci Quart. 40 (3), 203–211, 2002.
[6] Stanica, P. Cholesky factorizations of matrices associated with r th order recurrent sequences, Electron. J. Combin. Number Theory 5 (2), #A16, 2005.
[7] Zhizheng, Z. and Wang, X. A factorization of the symmetric Pascal matrix involving the Fibonacci matrix, Discrete Appl. Math. 155, 2371–2376, 2007.

APA	KILIÇ E, ÖMÜR N, TATAR G, ULUTAŞ Y (2009). Factorizations of the Pascal matrix via a generalized second order recurrent matrix. , 305 - 316.
Chicago	KILIÇ E.,ÖMÜR N.,TATAR G.,ULUTAŞ Y. T. Factorizations of the Pascal matrix via a generalized second order recurrent matrix. (2009): 305 - 316.
MLA	KILIÇ E.,ÖMÜR N.,TATAR G.,ULUTAŞ Y. T. Factorizations of the Pascal matrix via a generalized second order recurrent matrix. , 2009, ss.305 - 316.
AMA	KILIÇ E,ÖMÜR N,TATAR G,ULUTAŞ Y Factorizations of the Pascal matrix via a generalized second order recurrent matrix. . 2009; 305 - 316.
Vancouver	KILIÇ E,ÖMÜR N,TATAR G,ULUTAŞ Y Factorizations of the Pascal matrix via a generalized second order recurrent matrix. . 2009; 305 - 316.
IEEE	KILIÇ E,ÖMÜR N,TATAR G,ULUTAŞ Y "Factorizations of the Pascal matrix via a generalized second order recurrent matrix." , ss.305 - 316, 2009.
ISNAD	KILIÇ, E. vd. "Factorizations of the Pascal matrix via a generalized second order recurrent matrix". (2009), 305-316.

APA	KILIÇ E, ÖMÜR N, TATAR G, ULUTAŞ Y (2009). Factorizations of the Pascal matrix via a generalized second order recurrent matrix. Hacettepe Journal of Mathematics and Statistics, 38(3), 305 - 316.
Chicago	KILIÇ E.,ÖMÜR N.,TATAR G.,ULUTAŞ Y. T. Factorizations of the Pascal matrix via a generalized second order recurrent matrix. Hacettepe Journal of Mathematics and Statistics 38, no.3 (2009): 305 - 316.
MLA	KILIÇ E.,ÖMÜR N.,TATAR G.,ULUTAŞ Y. T. Factorizations of the Pascal matrix via a generalized second order recurrent matrix. Hacettepe Journal of Mathematics and Statistics, vol.38, no.3, 2009, ss.305 - 316.
AMA	KILIÇ E,ÖMÜR N,TATAR G,ULUTAŞ Y Factorizations of the Pascal matrix via a generalized second order recurrent matrix. Hacettepe Journal of Mathematics and Statistics. 2009; 38(3): 305 - 316.
Vancouver	KILIÇ E,ÖMÜR N,TATAR G,ULUTAŞ Y Factorizations of the Pascal matrix via a generalized second order recurrent matrix. Hacettepe Journal of Mathematics and Statistics. 2009; 38(3): 305 - 316.
IEEE	KILIÇ E,ÖMÜR N,TATAR G,ULUTAŞ Y "Factorizations of the Pascal matrix via a generalized second order recurrent matrix." Hacettepe Journal of Mathematics and Statistics, 38, ss.305 - 316, 2009.
ISNAD	KILIÇ, E. vd. "Factorizations of the Pascal matrix via a generalized second order recurrent matrix". Hacettepe Journal of Mathematics and Statistics 38/3 (2009), 305-316.