Tootfinder

This https://arxiv.org/abs/2401.15972 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Fibonacci vector and matrix p-norms
This paper delves into vector and matrix norms of Fibonacci numbers. Two classes of Fibonacci vectors and a parametric p-norm are defined. From this definition, several properties of Fibonacci vector and matrix p-norms are described by varying parameter p. A closed-form expression is given to obtain the value of p, setting the difference between the p-norm and the infinite norm below a given threshold. A new class of symmetric k-Fibonacci matrix is defined such that a simple reorganization simp…

Higher-order topology in Fibonacci quasicrystals
Chaozhi Ouyang, Qinghua He, Dong-Hui Xu, Feng Liu
https://arXiv.org/abs/2401.14896 https://

Higher-order topology in Fibonacci quasicrystals
In crystalline systems, higher-order topology, characterized by topological states of codimension greater than one, typically arises from the mismatch between Wannier centers and atomic sites, leading to filling anomalies. However, this phenomenon is less understood in aperiodic systems, such as quasicrystals, where Wannier centers are not well defined. In this study, we examine Fibonacci chains and squares, a quintessential type of quasicrystal, to investigate their higher-order topological pr…

This https://arxiv.org/abs/2307.05656 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

Universal stability of coherently diffusive 1D systems with respect to decoherence
Static disorder in a 3D crystal degrades the ideal ballistic dynamics until it produces a localized regime. This Metal-Insulator Transition is often preceded by coherent diffusion. By studying three paradigmatic 1D models, namely the Harper-Hofstadter-Aubry-André and Fibonacci tight-binding chains, along with the power-banded random matrix model, we show that whenever coherent diffusion is present, transport is exceptionally stable against decoherent noise. This is completely at odds with what…

The Fibonacci Lie algebra is not finitely presented
Dessislava H. Kochloukova, Victor Petrogradsky
https://arxiv.org/abs/2402.16098 https://

The Fibonacci Lie algebra is not finitely presented
We prove that the Fibonacci Lie algebra and the related just infinite self-similar Lie algebra are not finitely presented.

On a conjecture of E\v{g}ecio\v{g}lu and Ir\v{s}i\v{c}
Jianxin Wei, Yujun Yang
https://arXiv.org/abs/2401.14610 https://arXiv.org/pdf…

On a conjecture of Eǧecioǧlu and Iršič
In 2021, {Ö}. Eǧecioǧlu, V. Iršič introduced the concept of Fibonacci-run graph $\mathcal{R}_{n}$ as an induced subgraph of Hypercube. They conjectured that the diameter of $\mathcal{R}_{n}$ is given by $n-\lfloor(1+\frac{n}{2})^{\frac{1}{2}}-\frac{3}{4}\rfloor$. In this paper, we introduce the novel concept of distance-barriers between vertices in $\mathcal{R}_{n}$ and provide an elegant method to give lower bound for the diameter of $\mathcal{R}_{n}$ via distance-barriers. By constructin…

Counting points with Riemann-Roch formulas
Jorge Mart\'in-Morales
https://arxiv.org/abs/2402.18193 https://arxiv.org/pdf/2402.181…

Counting points with Riemann-Roch formulas
We provide an algorithm for computing the number of integral points lying in certain triangles that do not have integral vertices. We use techniques from Algebraic Geometry such as the Riemann-Roch formula for weighted projective planes and resolution of singularities. We analyze the complexity of the method and show that the worst case is given by the Fibonacci sequence. At the end of the manuscript a concrete example is developed in detail where the interplay with other invariants of singular…

On certain Fibonacci representations
K\'alm\'an Liptai, L\'aszl\'o N\'emeth, Tam\'as Szak\'acs, L\'aszl\'o Szalay
https://arxiv.org/abs/2403.15053

On certain Fibonacci representations
One of the most popular and studied recursive series is the Fibonacci sequence. It is challenging to see how Fibonacci numbers can be used to generate other recursive sequences. In our article, we describe some families of integer recurrence sequences as rational polynomial linear combinations of Fibonacci numbers.

Decompositions of hyperbolic Kac-Moody algebras with respect to imaginary root groups
Alex J. Feingold, Axel Kleinschmidt, Hermann Nicolai
https://arxiv.org/abs/2402.17737

Decompositions of hyperbolic Kac-Moody algebras with respect to imaginary root groups
We propose a novel way to define imaginary root subgroups associated with (timelike) imaginary roots of hyperbolic Kac-Moody algebras. Using in an essential way the theory of unitary irreducible representation of covers of the group SO(2,1), these imaginary root subgroups act on the complex Kac-Moody algebra viewed as a Hilbert space. We illustrate our new view on Kac-Moody groups by considering the example of a rank-two hyperbolic algebra that is related to the Fibonacci numbers. We also point…

This https://arxiv.org/abs/2403.14150 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csCC_…

A combinatorial view of Holant problems on higher domains
On the Boolean domain, there is a class of symmetric signatures called ``Fibonacci gates" for which a beautiful P-time combinatorial algorithm has been designed for the corresponding $\operatorname{Holant}^*$ problems. In this work, we give a combinatorial view for $\operatorname{Holant}^*(\mathcal{F})$ problems on a domain of size 3 where $\mathcal{F}$ is a set of arity 3 functions with inputs taking values on the domain of size 3 and the functions share some common properties. The combinato…

G\'en\'eralisation du Th\'eor\`eme de Zeckendorf
Rachid Chergui
https://arxiv.org/abs/2403.17292 https://arxiv.org/pdf/24…

Généralisation du Théorème de Zeckendorf
We consist of first presenting Zeckendorf Theorem with these two versions Fibonacci and Luca. In this document we obtain results on the generalized of the Zeckendorf theorem for Fibonacci numbers (multibonacci). Such results find applications in coding theory.

This https://arxiv.org/abs/2305.14422 has been replaced.
initial toot: https://mastoxiv.page/@arX…

Identifying non-Abelian anyons with upstream noise
Non-Abelian phases are among the most highly-sought states of matter, with those whose anyons permit universal quantum gates constituting the ultimate prize. The most promising candidate of such a phase is the fractional quantum Hall plateau at filling factors $ν=\frac{12}{5}$, which putatively facilitates Fibonacci anyons. Experimental validation of this assertion poses a major challenge and remains elusive. We present a measurement protocol that could achieve this goal with already-demonstra…

Some remarks regarding special elements in algebras obtained by the Cayley-Dickson process over Zp
Cristina Flaut, Andreea Baias
https://arxiv.org/abs/2403.18645

Some remarks regarding special elements in algebras obtained by the Cayley-Dickson process over Zp
In this paper we provide some properties of k-potent elements in algebras obtained by the Cayley-Dickson process over Zp. Moreover, we find a structure of nonunitary ring over Fibonacci quaternions over Z3 and we present a method to encrypt plain texts, by using invertible elements in such algebras.

"Die Fokusspirale" #Produktivität

Finding Fibonacci in the Hyperbolic Plane
MurphyKate Montee
https://arxiv.org/abs/2404.04389 https://arxiv.org/pdf/2404.04389<…

Finding Fibonacci in the Hyperbolic Plane
We use a combinatorial approximation of the hyperbolic plane to investigate properties of hyperbolic geometry such as exponential growth of perimeter and area of disks, and the linear isoperimetric inequality. This calculations give a surprising link to Fibonacci numbers.

Relations between Chebyshev, Fibonacci and Lucas polynomials via trigonometric sums
Lejla Smajlovi\'c, Zenan \v{S}abanac, Lamija \v{S}\'ceta
https://arxiv.org/abs/2403.12516

Relations between Chebyshev, Fibonacci and Lucas polynomials via trigonometric sums
In this paper we derive some new identities involving the Fibonacci and Lucas polynomials and the Chebyshev polynomials of the first and the second kind. Our starting point is a finite trigonometric sum which equals the resolvent kernel on the discrete circle with $m$ vertices and which can be evaluated in two different ways. An expression for this sum in terms of the Chebyshev polynomials was deduced in \cite{JKS} and the expression in terms of the Fibonacci and Lucas polynomials is deduced in…

Diagram model for the Okada algebra and monoid
Florent Hivert, Jeanne Scott
https://arxiv.org/abs/2404.16733 https://arxiv.org/pdf/24…

Diagram model for the Okada algebra and monoid
It is well known that the Young lattice is the Bratelli diagram of the symmetric groups expressing how irreducible representations restrict from $S_N$ to $S_{N-1}$. In 1988, Stanley discovered a similar lattice called the Young-Fibonacci lattice which was realized as the Bratelli diagram of a family of algebras by Okada in 1994. In this paper, we realize the Okada algebra and its associated monoid using a labeled version of Temperley-Lieb arc-diagrams. We prove in full generality that the dimen…

This https://arxiv.org/abs/2302.13647 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

String attractors of some simple-Parry automatic sequences
Firstly studied by Kempa and Prezza in 2018 as the cement of text compression algorithms, string attractors have become a compelling object of theoretical research within the community of combinatorics on words. In this context, they have been studied for several families of finite and infinite words. In this paper, we obtain string attractors of prefixes of particular infinite words generalizing k-bonacci words (including the famous Fibonacci word) and related to simple Parry numbers. In fact,…

Listening to fibonacci rabbits to hurry spring along a bit
* https://strudel.cc/?DNHyNT20ecou
* https://strudel.cc/?X7RVGQbevg7H

Three new classes of binomial Fibonacci sums
Robert Frontczak
https://arxiv.org/abs/2403.07878 https://arxiv.org/pdf/2403.07878

Three new classes of binomial Fibonacci sums
In this paper, we introduce three new classes of binomial sums involving Fibonacci (Lucas) numbers and weighted binomial coefficients.

Diagram model for the Okada algebra and monoid
Florent Hivert, Jeanne Scott
https://arxiv.org/abs/2404.16733 https://arxiv.org/pdf/24…

Diagram model for the Okada algebra and monoid
It is well known that the Young lattice is the Bratelli diagram of the symmetric groups expressing how irreducible representations restrict from $S_N$ to $S_{N-1}$. In 1988, Stanley discovered a similar lattice called the Young-Fibonacci lattice which was realized as the Bratelli diagram of a family of algebras by Okada in 1994. In this paper, we realize the Okada algebra and its associated monoid using a labeled version of Temperley-Lieb arc-diagrams. We prove in full generality that the dimen…

Fixed points of K-Fibonacci sequences
Brennan Benfield, Oliver Lippard
https://arxiv.org/abs/2404.08194 https://arxiv.org/pdf/2404.08…

Fixed points of K-Fibonacci sequences
A $K$-Fibonacci sequence is a binary recurrence sequence where $F_0=0$, $F_1=1$, and $F_n=K\cdot F_{n-1}+F_{n-2}$. These sequences are known to be periodic modulo every positive integer greater than $1$. If the length of one shortest period of a $K$-Fibonacci sequence modulo a positive integer is equal to the modulus, then that positive integer is called a $\textit{fixed point}$. This paper determines the fixed points of $K$-Fibonacci sequences according to the factorization of $K^2+4$ and conc…

This https://arxiv.org/abs/2311.05387 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On the Fibonacci tiling and its modern ramifications
In the last 30 years, the mathematical theory of aperiodic order has developed enormously. Many new tilings and properties have been discovered, few of which are covered or anticipated by the early papers and books. Here, we start from the well-known Fibonacci chain to explain some of them, with pointers to various generalisations as well as to higher-dimensional phenomena and results. This should give some entry points to the modern literature on the subject.

Slow relaxation of quasi-periodically driven integrable quantum many-body systems
Souradeep Ghosh, Sourav Bhattacharjee, Souvik Bandyopadhyay
https://arxiv.org/abs/2404.06667

Slow relaxation of quasi-periodically driven integrable quantum many-body systems
We study the emergence and stability of a prethermal phase in an integrable many-body system subjected to a Fibonacci drive. Despite not being periodic, Fibonacci drives have been shown to introduce dynamical constraints due to their self-similar structure, unlike random driving protocols. From perturbative analysis, this has been argued to result in an exponentially long prethermal phase in the high frequency limit of driving. Examining higher order terms in the perturbative expansion, we show…

This https://arxiv.org/abs/2306.08410 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Durfee rectangle identities as character identities for infinite Fibonacci configurations
We introduce a natural generalization of Maya diagrams -- the space of infinite Fibonacci configurations, which are specified functions on $\mathbb{Z}$ with values $1$ and $0$. Infinite Fibonacci configurations are particularly interesting as soon as they parametrize Feigin-Stoyanovsky type bases in lattice vertex superalgebras $V_{\sqrt{N}\mathbb{Z}}$ and their irreducible modules. We calculate the character of such configurations space by two different ways and obtain series of combinatorial …

Fixed points of K-Fibonacci sequences
Brennan Benfield, Oliver Lippard
https://arxiv.org/abs/2404.08194 https://arxiv.org/pdf/2404.08…

Fixed points of K-Fibonacci sequences
A $K$-Fibonacci sequence is a binary recurrence sequence where $F_0=0$, $F_1=1$, and $F_n=K\cdot F_{n-1}+F_{n-2}$. These sequences are known to be periodic modulo every positive integer greater than $1$. If the length of one shortest period of a $K$-Fibonacci sequence modulo a positive integer is equal to the modulus, then that positive integer is called a $\textit{fixed point}$. This paper determines the fixed points of $K$-Fibonacci sequences according to the factorization of $K^2+4$ and conc…

Anomalous Polarization in One-dimensional Aperiodic Insulators
A. Moustaj, J. P. J. Krebbekx, C. Morais Smith
https://arxiv.org/abs/2404.14916 https://

Anomalous Polarization in One-dimensional Aperiodic Insulators
By implementing a charge pumping scheme for one-dimensional aperiodic chains, we confirm the existence of topological phases in these systems whenever their finite-size realizations admit inversion symmetry. These phases are usually characterized by an anomalous edge response as a result of the bulk-boundary correspondence. We show that these signatures are all present in various chains, each representing a different class of structural aperiodicity: the Fibonacci quasicrystal, the Tribonacci q…

A combinatorial view of Holant problems on higher domains
Yin Liu
https://arxiv.org/abs/2403.14150 https://arxiv.org/pdf/2403.14150…

A combinatorial view of Holant problems on higher domains
On the Boolean domain, there is a class of symmetric signatures called ``Fibonacci gates" for which a beautiful P-time combinatorial algorithm has been designed for the corresponding $\operatorname{Holant}^*$ problems. In this work, we give a combinatorial view for $\operatorname{Holant}^*(\mathcal{F})$ problems on a domain of size 3 where $\mathcal{F}$ is a set of arity 3 functions with inputs taking values on the domain of size 3 and the functions share some common properties. The combinato…

This https://arxiv.org/abs/2306.08410 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Durfee rectangle identities as character identities for infinite Fibonacci configurations
We introduce a natural generalization of Maya diagrams -- the space of infinite Fibonacci configurations, which are specified functions on $\mathbb{Z}$ with values $1$ and $0$. Infinite Fibonacci configurations are particularly interesting as soon as they parametrize Feigin-Stoyanovsky type bases in lattice vertex superalgebras $V_{\sqrt{N}\mathbb{Z}}$ and their irreducible modules. We calculate the character of such configurations space by two different ways and obtain series of combinatorial …

Edit and Alphabet-Ordering Sensitivity of Lex-parse
Yuto Nakashima, Dominik K\"oppl, Mitsuru Funakoshi, Shunsuke Inenaga, Hideo Bannai
https://arxiv.org/abs/2402.19223

Edit and Alphabet-Ordering Sensitivity of Lex-parse
We investigate the compression sensitivity [Akagi et al., 2023] of lex-parse [Navarro et al., 2021] for two operations: (1) single character edit and (2) modification of the alphabet ordering, and give tight upper and lower bounds for both operations. For both lower bounds, we use the family of Fibonacci words. For the bounds on edit operations, our analysis makes heavy use of properties of the Lyndon factorization of Fibonacci words to characterize the structure of lex-parse.

This https://arxiv.org/abs/2404.01779 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

Diagonal Coset Approach to Topological Quantum Computation with Fibonacci Anyons
We investigate a promising conformal field theory realization scheme for topological quantum computation based on the Fibonacci anyons, which are believed to be realized as quasiparticle excitations in the $\mathbb{Z}_3$ parafermion fractional quantum Hall state in the second Landau level with filling factor $ν=12/5$. These anyons are non-Abelian and are known to be capable of universal topological quantum computation. The quantum information is encoded in the fusion channels of pairs of such …

General convolution sums involving Fibonacci m-step numbers
Robert Frontczak, Karol Gryszka
https://arxiv.org/abs/2403.19701 https://…

General convolution sums involving Fibonacci m-step numbers
In this paper, using a generating function approach, we derive several new convolution sum identities involving Fibonacci m-step numbers. As special instances of the results derived herein, we will get many new and known results involving Fibonacci, Tribonacci, Tetranacci and Pentanacci numbers. In addition, we establish some general results providing insights into the inner structure of such convolutions. Finally, some mixed convolutions involving Fibonacci m-step numbers and Jacobsthal and Pe…

This https://arxiv.org/abs/2401.08205 has been replaced.
link: https://scholar.google.com/scholar?q=a

A Pillai-Catalan-type problem involving Fibonacci numbers
This paper addresses A Pillai-Catalan-type problem assosiated with Fibonacci numbers. Let $F_{n}$ be the Fibonacci numbers defined by the recurrence relation $F_{1}=1$, $F_{2}=1$ and $F_{n}=F_{n-1}+F_{n-2}$ for all $n\geq 3$. We will find all positive integer solution to the equation $3^{x}-F_{n}2^{y}=1$ using properties of Fibonacci numbers, linear forms of logarithms, and the Baker-Davenport reduction method.

Superconductivity in the Fibonacci Chain
Ying Wang, Gautam Rai, Chris Matsumura, Anuradha Jagannathan, Stephan Haas
https://arxiv.org/abs/2403.06157 https:…

Superconductivity in the Fibonacci Chain
Superconductivity was recently reported in several quasicrystalline systems. These are materials which are structurally ordered, but since they are not translationally invariant, the usual BCS theory does not apply. At the present time, the underlying mechanism and the properties of the superconducting phase are insufficiently understood. To gain a better understanding of quasiperiodic superconductors, we consider the attractive Hubbard model on the Fibonacci chain, and examine its low-temperat…

Fibonacci vector and matrix p-norms
Francisco Salas-Molina
https://arXiv.org/abs/2401.15972 https://arXiv.org/pdf/2401.15972

Fibonacci vector and matrix p-norms
This paper delves into vector and matrix norms of Fibonacci numbers. Two classes of Fibonacci vectors and a parametric p-norm are defined. From this definition, several properties of Fibonacci vector and matrix p-norms are described by varying parameter p. A closed-form expression is given to obtain the value of p, setting the difference between the p-norm and the infinite norm below a given threshold. A new class of symmetric k-Fibonacci matrix is defined such that a simple reorganization simp…

This https://arxiv.org/abs/2306.11792 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

Complete Hilbert-Space Ergodicity in Quantum Dynamics of Generalized Fibonacci Drives
Ergodicity of quantum dynamics is often defined through statistical properties of energy eigenstates, as exemplified by Berry's conjecture in single-particle quantum chaos and the eigenstate thermalization hypothesis in many-body settings. In this work, we investigate whether quantum systems can exhibit a stronger form of ergodicity, wherein any time-evolved state uniformly visits the entire Hilbert space over time. We call such a phenomenon complete Hilbert-space ergodicity (CHSE), which is mo…

Walks on tiled boards
L\'aszl\'o N\'emeth
https://arxiv.org/abs/2403.12159 https://arxiv.org/pdf/2403.12159

Walks on tiled boards
Several articles deal with tilings with various shapes, and also a very frequent type of combinatorics is to examine the walks on graphs or on grids. We combine these two things and give the numbers of the shortest walks crossing the tiled $(1\times n)$ and $(2\times n)$ square grids by covering them with squares and dominoes. We describe these numbers not only recursively, but also as rational polynomial linear combinations of Fibonacci numbers.

This https://arxiv.org/abs/2401.17000 has been replaced.
initial toot: https://mastoxiv.page/@arX…

Multiple intermediate phases in the interpolating Aubry-André-Fibonacci model
We investigate a generalized interpolating Aubry-André-Fibonacci (IAAF) model with p-wave superconducting pairing. In the Aubry-André limit, we demonstrate that the system experiences transitions from a pure phase, either extended or critical, to a variety of intermediate phases and ultimately enters a localized phase with increasing potential strength. These intermediate phases include those with coexisting extended and localized states, extended and critical states, localized and critical s…

A generalization of a Ramanujan's exercise and Fibonacci polynomials
Genki Shibukawa
https://arxiv.org/abs/2403.06263 https://arx…

A generalization of a Ramanujan's exercise and Fibonacci polynomials
We give a generalization of a Ramanujan's exercise for high school students. Our results can be regarded as a variation of the factorization formula of $x^{n} - 1$.

This https://arxiv.org/abs/2403.06157 has been replaced.
initial toot: https://mastoxiv.page/@a…

Superconductivity in the Fibonacci Chain
Superconductivity was recently reported in several quasicrystalline systems. These are materials which are structurally ordered, but since they are not translationally invariant, the usual BCS theory does not apply. At the present time, the underlying mechanism and the properties of the superconducting phase are insufficiently understood. To gain a better understanding of quasiperiodic superconductors, we consider the attractive Hubbard model on the Fibonacci chain, and examine its low-temperat…

A generalization of a Ramanujan's exercise and Fibonacci polynomials
Genki Shibukawa
https://arxiv.org/abs/2403.06263 https://arx…

A generalization of a Ramanujan's exercise and Fibonacci polynomials
We give a generalization of a Ramanujan's exercise for high school students. Our results can be regarded as a variation of the factorization formula of $x^{n} - 1$.

Multiple intermediate phases in the interpolating Aubry-Andr\'{e}-Fibonacci model
Chenyue Guo
https://arXiv.org/abs/2401.17000 https://

Multiple intermediate phases in the interpolating Aubry-André-Fibonacci model
We investigate a generalized interpolating Aubry-André-Fibonacci (IAAF) model with p-wave superconducting pairing. In the Aubry-André limit, we demonstrate that the system experiences transitions from a pure phase, either extended or critical, to a variety of intermediate phases and ultimately enters a localized phase with increasing potential strength. These intermediate phases include those with coexisting extended and localized states, extended and critical states, localized and critical s…

This https://arxiv.org/abs/2403.06157 has been replaced.
initial toot: https://mastoxiv.page/@a…

Superconductivity in the Fibonacci Chain
Superconductivity was recently reported in several quasicrystalline systems. These are materials which are structurally ordered, but since they are not translationally invariant, the usual BCS theory does not apply. At the present time, the underlying mechanism and the properties of the superconducting phase are insufficiently understood. To gain a better understanding of quasiperiodic superconductors, we consider the attractive Hubbard model on the Fibonacci chain, and examine its low-temperat…

This https://arxiv.org/abs/2304.10426 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Binomial convolutions for rational power series
The binomial convolution of two sequences $\{a_n\}$ and $\{b_n\}$ is the sequence whose $n$th term is $\sum_{k=0}^{n} \binom{n}{k} a_k b_{n-k}$. If $\{a_n\}$ and $\{b_n\}$ have rational generating functions then so does their binomial convolution. We discuss an efficient method, using resultants, for computing this rational generating function and give several examples involving Fibonacci and tribonacci numbers and related sequences. We then describe a similar method for computing Hadamard prod…

This https://arxiv.org/abs/2312.07986 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On Diophantine equations with Fibonacci and Lucas sequences associated to Hardy-Ramanujan problem
In this paper, we deal with Diophantine equations $N = {F_k}^3 + {F_\ell }^3 = {F_m}^3 + {F_n}^3$ and $M = {L_k}^3 + {L_\ell }^3 = {L_m}^3 + {L_n}^3$. In other words, we discover the Fibonacci and Lucas numbers that are also Hardy-Ramanujan numbers.

Strong divisibility sequences and sieve methods
Tim Browning, Matteo Verzobio
https://arxiv.org/abs/2402.19301 https://arxiv.org/pdf/…

Strong divisibility sequences and sieve methods
We investigate strong divisibility sequences and produce lower and upper bounds for the density of integers in the sequence which only have (somewhat) large prime factors. We focus on the special cases of Fibonacci numbers and elliptic divisibility sequences, discussing the limitations of our methods. At the end of the paper there is an appendix by Sandro Bettin on divisor closed sets, that we use to study the density of prime terms that appear in strong divisibility sequences.