Exact and asymptotic solutions of a divide-and-conquer recurrence dividing at half: Theory and applications
HK Hwang, S Janson, TH Tsai - ACM Transactions on Algorithms (TALG), 2017 - dl.acm.org
Divide-and-conquer recurrences of the form f (n)= f (⌊ n/2⌋)+ f (⌈ n/2⌉)+ g (n)(n⩾ 2), with g
(n) and f (1) given, appear very frequently in the analysis of computer algorithms and related …
(n) and f (1) given, appear very frequently in the analysis of computer algorithms and related …
[HTML][HTML] Asymptotic expansions for linear homogeneous divide-and-conquer recurrences: Algebraic and analytic approaches collated
P Dumas - Theoretical Computer Science, 2014 - Elsevier
Among all sequences that satisfy a divide-and-conquer recurrence, those which are rational
with respect to a numeration system are certainly the most basic and the most essential …
with respect to a numeration system are certainly the most basic and the most essential …
A probabilistic approach to generalized Zeckendorf decompositions
I Ben-Ari, SJ Miller - SIAM Journal on Discrete Mathematics, 2016 - SIAM
Generalized Zeckendorf decompositions are expansions of integers as sums of elements of
solutions to recurrence relations. The simplest cases are base-b expansions, and the …
solutions to recurrence relations. The simplest cases are base-b expansions, and the …
Global extrema of the Delange function, bounds for digital sums and concave functions
OE Galkin, SY Galkina - Sbornik: Mathematics, 2020 - iopscience.iop.org
Abstract The sums $ S_ {q}(N) $ are defined by the equality $ S_ {q}(N)= s_q (1)+\dots+ s_q
(N-1) $ for all positive integers $ N $ and $ q\geqslant2 $, where $ s_q (n) $ is the sum of …
(N-1) $ for all positive integers $ N $ and $ q\geqslant2 $, where $ s_q (n) $ is the sum of …
Partial factorizations of products of binomial coefficients
L Du, JC Lagarias - International Journal of Number Theory, 2022 - World Scientific
Let G¯ n=∏ k= 0 nnk, the product of the elements of the n th row of Pascal's triangle. This
paper studies the partial factorizations of G¯ n given by the product G (n, x) of all prime …
paper studies the partial factorizations of G¯ n given by the product G (n, x) of all prime …
Partial factorizations of generalized binomial products
L Du, J Lagarias, W Yangjit - arXiv preprint arXiv:2112.14422, 2021 - arxiv.org
This paper studies an integer sequence $\overline {G} _n $ analogous to the product $
G_n=\prod_ {k= 0}^ n\binom {n}{k} $, the product of the elements of the $ n $-th row of …
G_n=\prod_ {k= 0}^ n\binom {n}{k} $, the product of the elements of the $ n $-th row of …
Hilbert's Inequality, Generalized Factorials, and Partial Factorizations of Generalized Binomial Products
W Yangjit - 2022 - deepblue.lib.umich.edu
This dissertation treats three topics in number theory. The first topic concerns the problem of
determining the optimal constant in the Montgomery–Vaughan weighted generalization of …
determining the optimal constant in the Montgomery–Vaughan weighted generalization of …
Normal distribution of correlation measures of binary sum-of-digits functions
J Emme, P Hubert - arXiv preprint arXiv:1810.11234, 2018 - arxiv.org
In this paper we study correlation measures introduced in\cite {emme_asymptotic_2017}.
Denote by $\mu_a (d) $ the asymptotic density of the set $\mathcal {E} _ {a, d}=\{n\in\mathbb …
Denote by $\mu_a (d) $ the asymptotic density of the set $\mathcal {E} _ {a, d}=\{n\in\mathbb …
[HTML][HTML] Power and exponential sums for generalized coding systems by a measure theoretic approach
Y Kamiya, T Okada, T Sekiguchi, Y Shiota - Theoretical Computer Science, 2015 - Elsevier
A measure theoretic approach to study the power and the exponential sums for the usual
coding system has been developed since the 1990s. In this paper, we first introduce a new …
coding system has been developed since the 1990s. In this paper, we first introduce a new …