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

Congruence properties for the partition function.

S Ahlgren1, K Ono

  • 1Department of Mathematics, University of Illinois, Urbana, IL 61801, USA.

Proceedings of the National Academy of Sciences of the United States of America
|October 19, 2001
PubMed
Summary
This summary is machine-generated.

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

Histochemical study of the lumbar colonic nerve supply to the internal anal sphincter and its physiological role in dogs.

Brain research·1992
Same author

[Analysis of pedestrian injuries in traffic accidents: impact point, injury portion, and injury severity].

Nihon hoigaku zasshi = The Japanese journal of legal medicine·1992
Same author

Immunolocalization of alkaline phosphatase in osteoblasts and matrix vesicles of human fetal bone.

Bone and mineral·1992
Same author

Changes of splenic lymphocyte subpopulation in mice inoculated with Babesia microti and Babesia rodhaini.

The Journal of veterinary medical science·1992
Same author

Magnocellular neurosecretory neurons with ferritin-like immunoreactivity in the hypothalamic supraoptic and paraventricular nuclei of the rat.

Brain research·1992
Same author

Gradient expression of neural cell adhesion molecule (NCAM) in the pontine migratory stream of fetal rats.

Neuroscience research·1992

Ramanujan-type congruences for the partition function are more common than previously thought. A new theoretical framework explains all known congruences, revealing their widespread nature.

Area of Science:

  • Number Theory
  • Combinatorics
  • Partition Theory

Background:

  • Srinivasa Ramanujan discovered congruences for the partition function modulo 5, 7, and 11.
  • For decades, few additional Ramanujan-type congruences were identified.
  • The rarity of these congruences suggested they might be isolated phenomena.

Purpose of the Study:

  • To investigate the prevalence of Ramanujan-type congruences for the partition function.
  • To develop a unifying theoretical framework for all known Ramanujan-type congruences.

Main Methods:

  • Analysis of the partition function and its properties.
  • Development of a novel theoretical framework to explain congruences.

Main Results:

Related Experiment Videos

  • Ramanujan-type congruences are significantly more widespread than previously documented.
  • A comprehensive theoretical framework has been established that accounts for all known congruences.
  • The study provides a unified explanation for these number theoretic properties.

Conclusions:

  • The phenomenon of Ramanujan-type congruences is not rare but widespread.
  • The developed theoretical framework offers a complete explanation for these congruences.
  • This research deepens the understanding of partition function properties and number theory.