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ARCHIV DER MATHEMATIK, ISSN 0003-889X, 08/2019, Volume 113, Issue 2, pp. 157 - 168
In order to investigate multiplicative structures in additively large sets, Beiglbock et al. raised a significant open question as to whether or not every... 
MATHEMATICS | Triveni triplet | Syndetic set | Geometric progression | Congruence
Journal Article
Periodica Mathematica Hungarica, ISSN 0031-5303, 6/2019, Volume 78, Issue 2, pp. 152 - 156
... density · Meager set Mathematics Subject Classification Primary 40A35; Secondary 11B05 · 54A20 1 Introduction Oxtoby’s classical book [14] examines analogues and non... 
54A20 | Statistical cluster points | Meager set | Statisical limit points | Mathematics, general | Mathematics | Primary 40A35 | Secondary 11B05 | Asymptotic density | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
Mathematika, ISSN 0025-5793, 01/2012, Volume 58, Issue 1, pp. 11 - 20
For a primitive root g modulo a prime p≥1 we obtain upper bounds on the gaps between the residues modulo p of the N consecutive powers agn, n=1,…,N, which is... 
11T23 (secondary) | 11A07 (primary) | 11B50 | 11B05 | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
The Rocky Mountain journal of mathematics, ISSN 0035-7596, 2018, Volume 48, Issue 6, pp. 1951 - 1961
We define a class of so-called thinnable ideals I on the positive integers which includes several well-known examples, e.g., the collection of sets with zero... 
Cluster point | Ideal convergence | Logarithmic density | Thinnable ideal | Summable ideal | Statistical convergence | Asymptotic density | Erdos-Ulam ideal | MATHEMATICS | summable ideal | ideal convergence | logarithmic density | CONVERGENT | statistical convergence | asymptotic density | thinnable ideal | SUBSEQUENCES
Journal Article
Mathematica Slovaca, ISSN 0139-9918, 06/2017, Volume 67, Issue 3, pp. 593 - 600
The concept of conditionally independent sets is introduced in this article. Its link with the concept of the conditional probability and with the concept of a... 
conditional probability | Primary 11B05 | independent events | asymptotic density | Secondary 60A05 | independent sets | Fuzzy sets | Set theory | Research | Mathematical research | Conditional probability
Journal Article
Journal of Number Theory, ISSN 0022-314X, 08/2014, Volume 141, pp. 136 - 158
A beautiful theorem of Zeckendorf states that every positive integer can be uniquely decomposed as a sum of non-consecutive Fibonacci numbers {Fn}, where F1=1,... 
Stirling numbers of the first kind | Gaussian behavior | Zeckendorf decompositions | Recurrence relations | MATHEMATICS | NUMBERS | EXPANSIONS | Mathematics - Number Theory
Journal Article
08/2015
Involve 10 (2017) 125-150 Zeckendorf's theorem states that every positive integer can be uniquely decomposed as a sum of nonconsecutive Fibonacci numbers,... 
Mathematics - Number Theory
Journal Article
Mathematica Slovaca, ISSN 0139-9918, 08/2018, Volume 68, Issue 4, pp. 717 - 726
Weighted uniform densities are a generalization of the uniform density, which is also known as the Banach density. In this paper, we introduce the concept of... 
filter | uniform density | Primary 11B05 | Darboux property | ideal | Secondary 40A35 | convergent series | ideal convergence | weighted uniform density | 40A05 | Banach density | P-ideal | MATHEMATICS | SERIES | CONVERGENCE | I-convergent series | Density | Sequences
Journal Article
Journal of Number Theory, ISSN 0022-314X, 05/2017, Volume 174, pp. 445 - 455
Let P(N) be the power set of N. An upper density (on N) is a nondecreasing and subadditive function μ⋆:P(N)→R such that μ⋆(N)=1 and μ⋆(k⋅X+h)=1kμ⋆(X) for all... 
Set functions | Darboux (or intermediate value) property | Asymptotic (or natural) density | Banach (or uniform) density | Subadditive functions | Upper and lower densities (and quasi-densities) | MATHEMATICS | INTEGERS
Journal Article
Monatshefte für Mathematik, ISSN 0026-9255, 11/2016, Volume 181, Issue 3, pp. 577 - 599
We provide a framework for proofs of structural theorems about sets with positive Banach logarithmic density. For example, we prove that if $$A\subseteq... 
Secondary 26E35 | Primary 11B05 | Logarithmic density | 37A45 | Nonstandard analysis | Mathematics, general | Mathematics | SUMSET PHENOMENON | MATHEMATICS | THEOREM | LARGE SETS | Computer science | Specific gravity | Analysis
Journal Article
Mathematica Slovaca, ISSN 0139-9918, 10/2017, Volume 67, Issue 5, pp. 1105 - 1128
In the present paper we introduce the upper and lower exponential density functions of subsets ⊆ ℕ*. We identify completely the form of the upper density and... 
upper and lower asymptotic density | abscissa of convergence | fractional density | 26A24 | upper and lower exponential density | Primary 11K99 | 26A03 | Dirichlet series | 26A15 | 26A48 | Secondary 11B05 | α-fractional density | MATHEMATICS | alpha-fractional density | Fuzzy sets | Set theory | Functions | Research | Functional equations | Mathematical research | Density
Journal Article
Positivity, ISSN 1385-1292, 3/2014, Volume 18, Issue 1, pp. 131 - 145
Journal Article
Mathematica Slovaca, ISSN 0139-9918, 10/2011, Volume 61, Issue 5, pp. 705 - 716
We investigate the sequence of integers x 1, x 2, x 3, … lying in {0, 1, …, [β]} in a so-called Rényi β-expansion of unity 1 = $\sum\limits_{j = 1}^\infty {x_j... 
transcendental numbers | Secondary 11B05, 11J82 | Algebra | β -expansion | Diophantine exponent | Mathematics, general | Mathematics | Primary 11A63 | β-expansion | MATHEMATICS | beta-expansion
Journal Article
Journal of Number Theory, ISSN 0022-314X, 2008, Volume 128, Issue 6, pp. 1646 - 1654
Let e ⩾ 1 and b ⩾ 2 be integers. For a positive integer n = ∑ j = 0 k a j × b j with 0 ⩽ a j < b , define S e , b ( n ) = ∑ j = 0 k a j e . n is called ( e , b... 
MATHEMATICS
Journal Article
Experimental Mathematics, ISSN 1058-6458, 01/2006, Volume 15, Issue 4, pp. 421 - 444
Digital snowflakes are solidifying cellular automata on the triangular lattice with the property that a site having exactly one occupied neighbor always... 
Secondary 68Q80, 11B05, 60K05 | macroscopic dynamics | exact solvability | thickness | growth model | Primary 37B15 | cellular automaton | Asymptotic density | Thickness | Cellular automaton | Growth model | Macroscopic dynamics | Exact solvability | MATHEMATICS | CELLULAR AUTOMATA | asymptotic density | 68Q80 | 60K05 | 37B15 | 11B05
Journal Article
Communications in Algebra, ISSN 0092-7872, 08/2019, Volume 47, Issue 8, pp. 3056 - 3063
Let denote the set of positive integers that appear as the strong symmetric genus of a finite nilpotent group. We show that if g is not congruent to , then .... 
strong symmetric genus | genus spectrum | nilpotent groups | Density | Primary 30F99 | Secondary 11B05 | MATHEMATICS | Integers | Lower bounds | Group theory
Journal Article
Journal of Number Theory, ISSN 0022-314X, 04/2019, Volume 197, pp. 218 - 227
The quotient set, or ratio set, of a set of integers A is defined asR(A):={a/b:a,b∈A,b≠0}. We consider the case in which A is the image of Z+ under a... 
p-adic numbers | Polynomials | Quotient set | Sum of powers | Denseness | MATHEMATICS
Journal Article
Mathematica Slovaca, ISSN 0139-9918, 10/2008, Volume 58, Issue 5, pp. 535 - 540
In the paper, there are proved some properties of the asymptotic density using the permutations. 
Primary 11B05 | Algebra | Mathematics, general | Mathematics | asymptotic density | Secondary 40C05 | permutation | DENSITY | MATHEMATICS
Journal Article
Archiv der Mathematik, ISSN 0003-889X, 4/2018, Volume 110, Issue 4, pp. 343 - 349
.... We study the notion of van der Corput sets with respect to general compact groups. Mathematics Subject Classification. Primary 11K06, Secondary 11B05, 37A45. Keywords... 
Uniform distribution | Compact groups | 37A45 | Van der Corput sets | Primary 11K06 | Mathematics, general | Van der Corput’s theorem | Intersective sets | Mathematics | Secondary 11B05 | MATHEMATICS | DIFFERENCE THEOREM | Van der Corput's theorem
Journal Article
Archiv der Mathematik, ISSN 0003-889X, 4/2017, Volume 108, Issue 4, pp. 341 - 350
... 11B05, 11N25, 11N37, 20F38, 30F99. Keywords. Strong symmetric genus, Riemann surface, Genus spectrum, Abelian groups, Asymptotic density, Unions of arithmetic... 
Primary 57M60 | Mathematics | 30F99 | Unions of arithmetic progressions | Secondary 11B05 | Riemann surface | 11N25 | Abelian groups | Mathematics, general | 20F38 | 11N37 | Strong symmetric genus | Genus spectrum | Asymptotic density | MATHEMATICS
Journal Article
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