Some New and Old Gibonacci Identities
Pankaj Jyoti Mahanta, Manjil P. Saikia
TL;DR
This paper offers new combinatorial interpretations of Lucas and Gibonacci numbers, leading to novel identities and simplified proofs of existing ones, while also discussing open problems in the area.
Contribution
It introduces new combinatorial perspectives on Lucas and Gibonacci numbers and derives new identities with simplified proofs.
Findings
New combinatorial interpretations of Lucas and Gibonacci numbers
Several new identities proved using these interpretations
Simplified proofs of existing identities
Abstract
We present a different combinatorial interpretations of Lucas and Gibonacci numbers. Using these interpretations we prove several new identities, and simplify the proofs of several known identities. Some open problems are discussed towards the end of the paper.
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Taxonomy
TopicsAdvanced Mathematical Theories and Applications · Advanced Mathematical Identities · Advanced Combinatorial Mathematics