The Generalized Bergman Game
B Baily, J Dell, I Durmić, H Fleischmann… - arXiv preprint arXiv …, 2021 - arxiv.org
Every positive integer may be written uniquely as a base-$\beta $ decomposition--that is a
legal sum of powers of $\beta $--where $\beta $ is the dominating root of a non-increasing …
legal sum of powers of $\beta $--where $\beta $ is the dominating root of a non-increasing …
The Bergman Game
B Baily, J Dell, I Durmić, HL Fleischmann… - The Fibonacci …, 2022 - Taylor & Francis
Every positive integer may be written uniquely as a base-φ decomposition–that is a legal
sum of powers of φ, the golden mean. Guided by earlier work on a two-player game which …
sum of powers of φ, the golden mean. Guided by earlier work on a two-player game which …
Central limit theorems for compound paths on the two-dimensional lattice
Zeckendorf proved that every integer can be written uniquely as a sum of nonconsecutive
Fibonacci numbers {Fn}, with later researchers showing that the distribution of the number of …
Fibonacci numbers {Fn}, with later researchers showing that the distribution of the number of …
Zeckendorf's theorem using indices in an arithmetic progression
Zeckendorf's Theorem states that any positive integer can be uniquely decomposed into a
sum of distinct, nonadjacent Fibonacci numbers. There are many generalizations, including …
sum of distinct, nonadjacent Fibonacci numbers. There are many generalizations, including …
On the Combinatorics of Placing Balls into Ordered Bins
In this paper, we use techniques of enumerative combinatorics to study the following
problem: we count the number of ways to split $ n $ balls into nonempty, ordered bins so that …
problem: we count the number of ways to split $ n $ balls into nonempty, ordered bins so that …
[PDF][PDF] BENJAMIN BAILY, JUSTINE DELL, IRFAN DURMI C, HENRY L. FLEISCHMANN, FAYE JACKSON, ISAAC MIJARES, STEVEN J. MILLER, ETHAN PESIKOFF …
I MIJARES - arXiv preprint arXiv:2109.00117, 2021 - academia.edu
Every positive integer may be written uniquely as a base-β decomposition–that is a legal
sum of powers of β–where β is the dominating root of a non-increasing positive linear …
sum of powers of β–where β is the dominating root of a non-increasing positive linear …
[PDF][PDF] On the Combinatorics of Placing Balls into Ordered Bins
In this paper, we use techniques of enumerative combinatorics to study the following
problem: we count the number of ways to split n balls into nonempty, ordered bins so that the …
problem: we count the number of ways to split n balls into nonempty, ordered bins so that the …