Linear vector recursions of arbitrary order

Faye, Bernadette and Németh, László and Szalay, László (2024) Linear vector recursions of arbitrary order. DISCRETE MATHEMATICS LETTERS, 2024 (13). pp. 50-57. ISSN 2664-2557

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Abstract

Solution of various combinatorial problems often requires vector recurrences of higher order (i.e., the order is larger than 1). Assume that there are given matrices A(1), A(2), ..., A(s), all from C-kxk. These matrices allow us to define the vector recurrence (v) over bar (n) = A(1)(v) over bar (n-1) +A(2)(v) over bar (n-2) + center dot center dot center dot + A(s)(v) over bar (n-s) for the vectors (v) over bar (n) is an element of C-k, n >= s. The paramount result of this paper is that we could separate the component sequences of the vectors and find a common linear recurrence relation to describe them. The principal advantage of our approach is a uniform treatment and the possibility of automatism. We could apply the main result to answer a problem that arose concerning the rows of the modified hyperbolic Pascal triangle with parameters {4, 5}. We also verified two other statements from the literature in order to illustrate the power of the method.

Tudományterület / tudományág

natural sciences > mathematics and computer sciences

Faculty

Not relevant

Institution

Soproni Egyetem

Item Type:	Article
Additional Information:	Funding Agency and Grant Number: Hungarian National Foundation for Scientific Research Grant [128088, 130909]; Slovak Scientific Grant Agency [VEGA 1/0776/21] Funding text: L. Szalay was supported by the Hungarian National Foundation for Scientific Research Grant No. 128088, and No. 130909, and by the Slovak Scientific Grant Agency VEGA 1/0776/21. This paper was partially written when the third author visited the African Institute for Mathematical Sciences in Senegal. He is grateful for the great hospitality in Mbour.
SWORD Depositor:	Teszt Sword
Depositing User:	Csaba Horváth
Identification Number:	MTMT:34866301
Date Deposited:	24 May 2024 11:11
Last Modified:	24 May 2024 11:11
URI:	http://publicatio.uni-sopron.hu/id/eprint/3195

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