Sequences Generated by the Lattice Path Problem with Various Vector Sets
Abstract
The lattice path problem involves finding a path between two specific points in space using only certain predefined vectors. The goal is to establish a relationship between the number of lattice paths to a point and the emergence of specific number sequences. This was achieved by analyzing lattice paths in a table within a cartesian coordinate system. The number of paths to a particular cell, starting from the first column of the table, was computed, and the results were analyzed through a computer program.This method revealed Fibonacci, Pell, Pell-Lucas, and Tribonacci sequences.Upon examining tables in dimensions higher than two, it was observed that the numbers found corresponded to the products of these special number sequences. Recursive relations were derived for the vector sets used in this process, and through these relations, identities among the number sequences were established.
Keywords
References
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Details
Primary Language
English
Subjects
Algebra and Number Theory, Combinatorics and Discrete Mathematics (Excl. Physical Combinatorics)
Journal Section
Research Article
Publication Date
December 31, 2024
Submission Date
December 6, 2024
Acceptance Date
December 29, 2024
Published in Issue
Year 2024 Volume: 1 Number: 1
APA
Karaçam, C., & Vural, A. (2024). Sequences Generated by the Lattice Path Problem with Various Vector Sets. Türkiye Mathematical Sciences, 1(1), 39-70. https://izlik.org/JA78KK27LR
AMA
1.Karaçam C, Vural A. Sequences Generated by the Lattice Path Problem with Various Vector Sets. TMS. 2024;1(1):39-70. https://izlik.org/JA78KK27LR
Chicago
Karaçam, Cemil, and Alper Vural. 2024. “Sequences Generated by the Lattice Path Problem With Various Vector Sets”. Türkiye Mathematical Sciences 1 (1): 39-70. https://izlik.org/JA78KK27LR.
EndNote
Karaçam C, Vural A (December 1, 2024) Sequences Generated by the Lattice Path Problem with Various Vector Sets. Türkiye Mathematical Sciences 1 1 39–70.
IEEE
[1]C. Karaçam and A. Vural, “Sequences Generated by the Lattice Path Problem with Various Vector Sets”, TMS, vol. 1, no. 1, pp. 39–70, Dec. 2024, [Online]. Available: https://izlik.org/JA78KK27LR
ISNAD
Karaçam, Cemil - Vural, Alper. “Sequences Generated by the Lattice Path Problem With Various Vector Sets”. Türkiye Mathematical Sciences 1/1 (December 1, 2024): 39-70. https://izlik.org/JA78KK27LR.
JAMA
1.Karaçam C, Vural A. Sequences Generated by the Lattice Path Problem with Various Vector Sets. TMS. 2024;1:39–70.
MLA
Karaçam, Cemil, and Alper Vural. “Sequences Generated by the Lattice Path Problem With Various Vector Sets”. Türkiye Mathematical Sciences, vol. 1, no. 1, Dec. 2024, pp. 39-70, https://izlik.org/JA78KK27LR.
Vancouver
1.Cemil Karaçam, Alper Vural. Sequences Generated by the Lattice Path Problem with Various Vector Sets. TMS [Internet]. 2024 Dec. 1;1(1):39-70. Available from: https://izlik.org/JA78KK27LR