Results 31 to 40 of about 10,730 (186)
Restricted Permutations, Fibonacci Numbers, and k-generalized Fibonacci Numbers
, 2002 A permutation $ \in S_n$ is said to {\it avoid} a permutation $ \in S_k$ whenever $ $ contains no subsequence with all of the same pairwise comparisons as $ $. For any set $R$ of permutations, we write $S_n(R)$ to denote the set of permutations in $S_n$ which avoid every permutation in $R$. In 1985 Simion and Schmidt showed that $|S_n(132, 213, 123)
Egge, Eric S., Mansour, Toufik
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Inversion Polynomials for Permutations Avoiding Consecutive Patterns [PDF]
, 2014 In 2012, Sagan and Savage introduced the notion of $st$-Wilf equivalence for a statistic $st$ and for sets of permutations that avoid particular permutation patterns which can be extended to generalized permutation patterns.
Cameron, Naiomi, Killpatrick, Kendra
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Bernoulli F-polynomials and Fibo–Bernoulli matrices
Advances in Difference Equations, 2019 In this article, we define the Euler–Fibonacci numbers, polynomials and their exponential generating function. Several relations are established involving the Bernoulli F-polynomials, the Euler–Fibonacci numbers and the Euler–Fibonacci polynomials. A new
Semra Kuş, Naim Tuglu, Taekyun Kim
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On $k$-Fibonacci balancing and $k$-Fibonacci Lucas-balancing numbers
Karpatsʹkì Matematičnì Publìkacìï, 2021 The balancing number $n$ and the balancer $r$ are solution of the Diophantine equation $$1+2+\cdots+(n-1) = (n+1)+(n+2)+\cdots+(n+r). $$ It is well known that if $n$ is balancing number, then $8n^2 + 1$ is a perfect square and its positive square root is
S.E. Rihane
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Nature-Inspired Design Strategies for Efficient Atmospheric Water Harvesting. [PDF]
Adv MaterThis review presents advances in bioinspired atmospheric water harvesting systems, emphasizing how structural motifs such as wettability gradients, directional transport, and hierarchical porosity have been translated into engineered fog‐collection and vapor‐sorption strategies for enhanced water uptake, accelerated transport, and energy‐efficient ...
Lee Y, Lee Y, Fan S, Yang S.
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On Generalized Fibonacci Numbers [PDF]
The American Mathematical Monthly, 1971 (1971). On Generalized Fibonacci Numbers. The American Mathematical Monthly: Vol. 78, No. 10, pp. 1108-1109.
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On (k,p)-Fibonacci numbers and matrices [PDF]
Notes on Number Theory and Discrete MathematicsIn this paper, some relations between the powers of any matrices X satisfying the equation Xᵏ-pXᵏ⁻¹-(p-1)X-I=0 and (k,p)-Fibonacci numbers are established with ...
Sinan Karakaya +2 more
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On Generalized Jacobsthal and Jacobsthal–Lucas Numbers
Annales Mathematicae Silesianae, 2022 Jacobsthal numbers and Jacobsthal–Lucas numbers are some of the most studied special integer sequences related to the Fibonacci numbers. In this study, we introduce one parameter generalizations of Jacobsthal numbers and Jacobsthal–Lucas numbers.
Bród Dorota, Michalski Adrian
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On the bounds for the spectral norms of geometric circulant matrices
Journal of Inequalities and Applications, 2016 In this paper, we define a geometric circulant matrix whose entries are the generalized Fibonacci numbers and hyperharmonic Fibonacci numbers. Then we give upper and lower bounds for the spectral norms of these matrices.
Can Kızılateş, Naim Tuglu
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Bi-Periodic (p,q)-Fibonacci and Bi-Periodic (p,q)-Lucas Sequences
Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 2023 In this paper, we define bi-periodic (p,q)-Fibonacci and bi-periodic (p,q)-Lucas sequences, which generalize Fibonacci type, Lucas type, bi-periodic Fibonacci type and bi-periodic Lucas type sequences, using recurrence relations of (p,q)-Fibonacci and (p,
Yasemin Taşyurdu +1 more
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