Patrick Dynes
YOU?
Author Swipe
View article: A $p$-adic Perron–Frobenius theorem
A $p$-adic Perron–Frobenius theorem Open
We prove that if an $n\times n$ matrix defined over ${\mathbb Q}_p$ (or more generally an arbitrary complete, discretely-valued, non-Archimedean field) satisfies a certain congruence property, then it has a strictly maximal eigenvalue in $…
View article: The emergence of 4-cycles in polynomial maps over the extended integers
The emergence of 4-cycles in polynomial maps over the extended integers Open
Let $f(x) \in \mathbb{Z}[x]$; for each integer $α$ it is interesting to consider the number of iterates $n_α$, if possible, needed to satisfy $f^{n_α}(α) = α$. The sets $\{α, f(α), \ldots, f^{n_α - 1}(α), α\}$ generated by the iterates of …
View article: Gaussian Distribution of the Number of Summands in Generalized Zeckendorf Decompositions in Small Intervals
Gaussian Distribution of the Number of Summands in Generalized Zeckendorf Decompositions in Small Intervals Open
Zeckendorf's theorem states that every positive integer can be written uniquely as a sum of non-consecutive Fibonacci numbers ${F_n}$, with initial terms $F_1 = 1, F_2 = 2$. Previous work proved that as $n \to \infty$ the distribution of t…
View article: Gaussian Distribution of the Number of Summands in Generalized\n Zeckendorf Decompositions in Small Intervals
Gaussian Distribution of the Number of Summands in Generalized\n Zeckendorf Decompositions in Small Intervals Open
Zeckendorf's theorem states that every positive integer can be written\nuniquely as a sum of non-consecutive Fibonacci numbers ${F_n}$, with initial\nterms $F_1 = 1, F_2 = 2$. Previous work proved that as $n \\to \\infty$ the\ndistribution…