Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Numerical Calculations01:24

Numerical Calculations

388
In engineering applications, the representation of the numerical value is critical. Presenting or reporting the answer is one of the essential parts of engineering practices. Numerical calculations are performed using handheld calculators or computers since numerically accurate answers are always preferred.
The solution to a problem is obtained using different methods. While manually solving algebraic symbols is one of the most common methods, the graphical method is often preferred. Computers...
388
Arithmetic Mean01:08

Arithmetic Mean

14.8K
The arithmetic mean is the most commonly used measure of the central tendency of a data set. It is defined as the sum of all the elements constituting the data set, divided by the total number of elements. It is sometimes loosely referred to as the “average.”
When all the values in a data set are not unique, the sum in the numerator can be calculated by multiplying each distinct value by its frequency.
Sometimes, the arithmetic mean of a sample can be affected by a few data points...
14.8K
How Data are Classified: Numerical Data00:59

How Data are Classified: Numerical Data

29.7K
Data that are countable or measurable in specific units are called numerical or quantitative data. Quantitative data are always numbers. Quantitative data are the result of counting or measuring the attributes of a population. Amount of money, pulse rate, weight, number of people living in a town, and number of students who opt for statistics are examples of quantitative data.
Quantitative data may be either discrete or continuous. All quantitative data that take on only specific numerical...
29.7K
Geometric Mean01:15

Geometric Mean

3.4K
The mean is a measure of the central tendency of a data set. In some data sets, the data is inherently multiplicative, and the arithmetic mean is not useful. For example, the human population multiplies with time, and so does the credit amount of financial investment, as the interest compounds over successive time intervals.
In cases of multiplicative data, the geometric mean is used for statistical analysis. First, the product of all the elements is taken. Then, if there are n elements in the...
3.4K
Basic Discrete Time Signals01:16

Basic Discrete Time Signals

251
The unit step sequence is defined as 1 for zero and positive values of the integer n. This sequence can be graphically displayed using a set of eight sample points, showing a step function starting from n=0 and remaining constant thereafter.
The unit impulse or sample sequence is mathematically expressed as zero for all n values except at n=0, where it is one. The unit impulse sequence, denoted by δ(n), is the first difference of the unit step sequence, while the unit step sequence u(n) is...
251
Determination of Pi Terms01:15

Determination of Pi Terms

321
The Buckingham Pi theorem is a valuable method in dimensional analysis, reducing complex relationships between variables into dimensionless terms. Relevant variables in analyzing the lift force on an airplane wing include lift force, air density, wing area, aircraft velocity, and air viscosity. Expressing each variable in terms of fundamental dimensions — mass, length, and time — provides a consistent foundation for constructing these dimensionless terms.
The theorem indicates that...
321

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Asymptotic Analysis of <i>q</i>-Recursive Sequences.

Algorithmica·2022
Same author

Caps and progression-free sets in <math></math>.

Designs, codes, and cryptography·2020
Same journal

LRCS: Duality, LP bounds, and field size.

Designs, codes, and cryptography·2026
Same journal

Information-set decoding for convolutional codes.

Designs, codes, and cryptography·2025
Same journal

Knot theory and error-correcting codes.

Designs, codes, and cryptography·2025
Same journal

New results on non-disjoint and classical strong external difference families.

Designs, codes, and cryptography·2025
Same journal

Guessing less and better: improved attacks on GIFT-64.

Designs, codes, and cryptography·2025
Same journal

Conjunctive hierarchical secret sharing by finite geometry.

Designs, codes, and cryptography·2025
See all related articles

Related Experiment Video

Updated: Aug 3, 2025

Multimedia Battery for Assessment of Cognitive and Basic Skills in Mathematics BM-PROMA
10:58

Multimedia Battery for Assessment of Cognitive and Basic Skills in Mathematics BM-PROMA

Published on: August 28, 2021

4.6K

Large subsets of  without arithmetic progressions.

Christian Elsholtz1, Benjamin Klahn1, Gabriel F Lipnik1

  • 1Graz University of Technology, Graz, Austria.

Designs, Codes, and Cryptography
|April 10, 2023
PubMed
Summary
This summary is machine-generated.

Researchers established new lower bounds for progression-free sets in integers. These findings improve understanding of combinatorial number theory and the structure of sets avoiding arithmetic progressions.

Keywords:
Arithmetic progressionsBehrend-type constructionProgression-free sets

More Related Videos

Universal Screening for Prevention of Reading, Writing, and Math Disabilities in Spanish
14:43

Universal Screening for Prevention of Reading, Writing, and Math Disabilities in Spanish

Published on: July 18, 2020

8.1K
Generating Strictly Controlled Stimuli for Figure Recognition Experiments
05:39

Generating Strictly Controlled Stimuli for Figure Recognition Experiments

Published on: March 18, 2019

5.3K

Related Experiment Videos

Last Updated: Aug 3, 2025

Multimedia Battery for Assessment of Cognitive and Basic Skills in Mathematics BM-PROMA
10:58

Multimedia Battery for Assessment of Cognitive and Basic Skills in Mathematics BM-PROMA

Published on: August 28, 2021

4.6K
Universal Screening for Prevention of Reading, Writing, and Math Disabilities in Spanish
14:43

Universal Screening for Prevention of Reading, Writing, and Math Disabilities in Spanish

Published on: July 18, 2020

8.1K
Generating Strictly Controlled Stimuli for Figure Recognition Experiments
05:39

Generating Strictly Controlled Stimuli for Figure Recognition Experiments

Published on: March 18, 2019

5.3K

Area of Science:

  • Combinatorial Number Theory
  • Set Theory
  • Harmonic Analysis

Background:

  • The study of arithmetic progressions is a fundamental problem in number theory.
  • Finding maximal sets free from arithmetic progressions (AP) is a challenging task.
  • Existing bounds for the size of such sets are often difficult to improve.

Purpose of the Study:

  • To establish improved lower bounds for the size of progression-free sets in integers.
  • To construct explicit examples of large progression-free sets.
  • To advance the understanding of Behrend construction and its variations.

Main Methods:

  • Construction of explicit progression-free sets using number-theoretic techniques.
  • Analysis of the properties of these constructed sets concerning arithmetic progressions.
  • Application of techniques from harmonic analysis and additive combinatorics.

Main Results:

  • Improved lower bounds for the size of k-term progression-free sets in {1, ..., N}.
  • Specific bounds derived for odd and even values of m, related to the least prime factor.
  • Demonstration of new explicit constructions that outperform previous results for certain parameters.

Conclusions:

  • The constructed sets provide significant improvements on known lower bounds for progression-free sets.
  • The results contribute to the ongoing effort to determine the precise behavior of the maximum size of such sets.
  • Further research directions include exploring these constructions for different settings and refining the bounds.