Zobrazeno 1 - 10
of 103
pro vyhledávání: '"Vandehey, Joseph"'
A classic theorem of Uchimura states that the difference between the sum of the smallest parts of the partitions of $n$ into an odd number of distinct parts and the corresponding sum for an even number of distinct parts is equal to the number of divi
Externí odkaz:
http://arxiv.org/abs/2402.12549
Let $p_{\textrm{dsd}} (n)$ be the number of partitions of $n$ into distinct squarefree divisors of $n$. In this note, we find a lower bound for $p_{\textrm{dsd}} (n)$, as well as a sequence of $n$ for which $p_{\textrm{dsd}} (n)$ is unusually large.<
Externí odkaz:
http://arxiv.org/abs/2402.08119
We show that the number of short binary signed-digit representations of an integer $n$ is equal to the $n$-th term in the Stern sequence. Various proofs are provided, including direct, bijective, and generating function proofs. We also show that this
Externí odkaz:
http://arxiv.org/abs/2308.07448
Autor:
Lukyanenko, Anton, Vandehey, Joseph
We prove a suite of dynamical results, including exactness of the transformation and piecewise-analyticity of the invariant measure, for a family of continued fraction systems, including specific examples over reals, complex numbers, quaternions, oct
Externí odkaz:
http://arxiv.org/abs/2303.02249
Autor:
Lukyanenko, Anton, Vandehey, Joseph
We prove the convergence of a wide class of continued fractions, including generalized continued fractions over quaternions and octonions. Fractional points in these systems are not bounded away from the unit sphere, so that the iteration map is not
Externí odkaz:
http://arxiv.org/abs/2205.12801
We show that normality for continued fractions expansions and normality for base-$b$ expansions are maximally logically separate. In particular, the set of numbers that are normal with respect to the continued fraction expansion but not base-$b$ norm
Externí odkaz:
http://arxiv.org/abs/2111.11522
A classical Kamae-Weiss theorem states that an increasing sequence $(n_i)_{i\in\mathbb N}$ of positive lower density is \emph{normality preserving}, i.e. has the property that for any normal binary sequence $(b_n)_{n\in\mathbb N}$, the sequence $(b_{
Externí odkaz:
http://arxiv.org/abs/2004.02811
Akademický článek
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Autor:
Carton, Olivier, Vandehey, Joseph
We give two different proofs of the fact that non-oblivious selection via regular group sets preserves normality. Non-oblivious here means that whether or not a symbol is selected can depend on the symbol itself. One proof relies on the incompressibi
Externí odkaz:
http://arxiv.org/abs/1905.05801
Autor:
Hiary, Ghaith, Vandehey, Joseph
We study the density of the invariant measure of the Hurwitz complex continued fraction from a computational perspective. It is known that this density is piece-wise real-analytic and so we provide a method for calculating the Taylor coefficients aro
Externí odkaz:
http://arxiv.org/abs/1805.10151