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On a Generalized Fibonacci Recurrence

Research output: Contribution to Journal/Magazine › Journal article

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On a Generalized Fibonacci Recurrence. / Blitvic, Natasha; Fernandez, Vicente.
In: arXiv, 13.01.2020.

Research output: Contribution to Journal/Magazine › Journal article

Harvard

Blitvic, N & Fernandez, V 2020, 'On a Generalized Fibonacci Recurrence', arXiv. <https://arxiv.org/abs/1901.04080>

APA

Blitvic, N., & Fernandez, V. (2020). On a Generalized Fibonacci Recurrence. arXiv. https://arxiv.org/abs/1901.04080

Vancouver

Blitvic N, Fernandez V. On a Generalized Fibonacci Recurrence. arXiv. 2020 Jan 13.

Author

Blitvic, Natasha ; Fernandez, Vicente. / On a Generalized Fibonacci Recurrence. In: arXiv. 2020.

Bibtex

@article{cb5ce2ef1f4d40a5bbf965dd32a66637,
title = "On a Generalized Fibonacci Recurrence",
abstract = "The generalized Fibonacci recurrence gn=gn−k+gn−m was recently used to demonstrate the theoretically optimal nature of limited senescence in morphologically symmetrically dividing bacteria. Here, we study this recurrence from a more abstract viewpoint, as a general model for asymmetric branching, and interpret solutions for different initial conditions in terms of branching-related quantities. We provide a compact diagrammatic representation for the evolution of this process which leads to an explicit binomial identity for the sums of elements lying on the diagonals kx+my=n in Pascal's triangle N0×N0∋(x,y)↦(x+yx), previously sought by Dickinson [Dic50], Raab [Raa63], and Green [Gre68].",
author = "Natasha Blitvic and Vicente Fernandez",
year = "2020",
month = jan,
day = "13",
language = "English",
journal = "arXiv",

}

RIS

TY - JOUR

T1 - On a Generalized Fibonacci Recurrence

AU - Blitvic, Natasha

AU - Fernandez, Vicente

PY - 2020/1/13

Y1 - 2020/1/13

N2 - The generalized Fibonacci recurrence gn=gn−k+gn−m was recently used to demonstrate the theoretically optimal nature of limited senescence in morphologically symmetrically dividing bacteria. Here, we study this recurrence from a more abstract viewpoint, as a general model for asymmetric branching, and interpret solutions for different initial conditions in terms of branching-related quantities. We provide a compact diagrammatic representation for the evolution of this process which leads to an explicit binomial identity for the sums of elements lying on the diagonals kx+my=n in Pascal's triangle N0×N0∋(x,y)↦(x+yx), previously sought by Dickinson [Dic50], Raab [Raa63], and Green [Gre68].

AB - The generalized Fibonacci recurrence gn=gn−k+gn−m was recently used to demonstrate the theoretically optimal nature of limited senescence in morphologically symmetrically dividing bacteria. Here, we study this recurrence from a more abstract viewpoint, as a general model for asymmetric branching, and interpret solutions for different initial conditions in terms of branching-related quantities. We provide a compact diagrammatic representation for the evolution of this process which leads to an explicit binomial identity for the sums of elements lying on the diagonals kx+my=n in Pascal's triangle N0×N0∋(x,y)↦(x+yx), previously sought by Dickinson [Dic50], Raab [Raa63], and Green [Gre68].

M3 - Journal article

JO - arXiv

JF - arXiv

ER -