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 Experiment Videos

Ramsey's Theorem for a Class of Categories.

R L Graham1, K Leeb, B L Rothschild

  • 1Bell Telephone Laboratories, Murray Hill, New Jersey 07974.

Proceedings of the National Academy of Sciences of the United States of America
|January 1, 1972
PubMed
Summary

This study generalizes Ramsey's Theorem for specific categories, proving the vector space analogue and implications for n-parameter sets. It confirms Rota's conjecture and Rado's results on linear equations and van der Waerden's theorem.

Related Concept Videos

You might also read

Related Articles

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

Sort by
Same author

Clinical Pharmacogenetics Implementation Consortium (CPIC) Guideline for CYP2D6 and CYP2C19 Genotypes and Dosing of Selective Serotonin Reuptake Inhibitors.

Clinical pharmacology and therapeutics·2015
Same author

A mass spectrometer investigation of the isotopes of xenon and krypton resulting from the fission of U225 by thermal neutrons.

Canadian journal of research·2010
Same author

[Sentinel lymph node dissection for localized prostate cancer].

Actas urologicas espanolas·2007
Same author

Health human resource planning: head counting is not enough.

Hospital quarterly·2002
Same author

[Laparoscopic tumor nephrectomy].

Der Urologe. Ausg. A·2002
Same author

Postablative risk of endometrial carcinoma in New Zealand white rabbits given high-dose estrogen.

The Journal of reproductive medicine·2000

Area of Science:

  • Combinatorics
  • Set Theory
  • Linear Algebra

Background:

  • Ramsey's Theorem guarantees monochromatic subsets under specific conditions.
  • Generalizations of Ramsey's Theorem are crucial for advancing combinatorial mathematics.
  • Rota's conjecture proposed a vector space analogue to Ramsey's Theorem.

Purpose of the Study:

  • To establish a generalized theorem extending Ramsey's Theorem.
  • To prove the vector space analogue of Ramsey's Theorem, confirming G-C. Rota's conjecture.
  • To demonstrate implications for n-parameter sets, including van der Waerden's and Rado's theorems.

Main Methods:

  • The study employs abstract mathematical reasoning and proof techniques.
  • It focuses on developing a generalized theorem within specific mathematical categories.

Related Experiment Videos

  • The methodology involves leveraging existing theorems and conjectures in combinatorics and linear algebra.

    • Main Results:

    • A new theorem is established that generalizes Ramsey's Theorem.
    • The vector space analogue of Ramsey's Theorem is proven true.
    • The generalized theorem implies van der Waerden's theorem and Rado's results.

    Conclusions:

    • The established theorem provides a significant advancement in Ramsey theory.
    • The confirmation of Rota's conjecture has broad implications for vector space analogues.
    • This work unifies several important results in combinatorial number theory and linear algebra.