Trying to track down a Partition theorem

Click For Summary
SUMMARY

The discussion revolves around a partition theorem in mathematics that pertains to proving theorems for all but a finite number of cases. The theorem in question involves partitioning numbers, specifically mentioning the number of ways to partition with either 17 or 19 bins, resulting in 237 ways except for a finite number of exceptions. This concept aligns with "almost everywhere" theorems commonly used in number theory, which assert that certain properties hold true for all cases except for a limited set of exceptions. The participants express a need for more specific details to accurately identify the theorem discussed.

PREREQUISITES
  • Understanding of partition theory in mathematics
  • Familiarity with number theory concepts
  • Knowledge of "almost everywhere" theorems
  • Basic mathematical proof techniques
NEXT STEPS
  • Research specific partition theorems in number theory
  • Explore the concept of "almost everywhere" theorems
  • Study the implications of finite exceptions in mathematical proofs
  • Investigate the historical context of partition theory developments
USEFUL FOR

Mathematicians, students of number theory, and anyone interested in advanced mathematical proofs and theorems related to partitioning numbers.

selfAdjoint
Staff Emeritus
Gold Member
Dearly Missed
Messages
6,843
Reaction score
11
Years ago I read in the daily paper(!) an account of a new theorem in partition theory. The key was that the guy had had the idea of proving theorems that were not for all cases but for all but a finite number of cases. The theorem had something about the number of ways to partion (prime?) numbers, and all I remember is that when the number of partitioning bins was either 17 or 19 (I forget), the number of ways was 237 "for all numbers except in a finite number of cases". You can see how confused I am. The fault is not the original story, which I remember as being pretty clear, but the long memory gap.


Does this ring a bell for anybody?
 
Physics news on Phys.org
Daily problem is that, The math problem is in some famour mind

I see, some simple problem is fun very. but it is mean sole.
As some mean enough math question is to let it free fly... .
 


I'm not familiar with a specific partition theorem that fits this description, but it does sound like the concept of "almost everywhere" theorems in mathematics. These are theorems that hold true for all cases except for a finite number of exceptions. This approach is often used in number theory, where it is impossible to prove a theorem for all numbers due to the infinite nature of numbers. Instead, mathematicians prove the theorem for all but a finite number of cases, which is still considered a strong result. If you can provide more specific details or keywords, I may be able to help you track down the theorem you're looking for.
 

Similar threads

  • · Replies 3 ·
Replies
3
Views
1K
  • · Replies 14 ·
Replies
14
Views
3K
  • · Replies 9 ·
Replies
9
Views
2K
  • · Replies 5 ·
Replies
5
Views
6K
  • · Replies 4 ·
Replies
4
Views
5K
  • · Replies 3 ·
Replies
3
Views
3K
  • · Replies 12 ·
Replies
12
Views
2K
  • · Replies 9 ·
Replies
9
Views
2K
  • · Replies 68 ·
3
Replies
68
Views
12K
  • · Replies 113 ·
4
Replies
113
Views
11K