Trying to track down a Partition theorem

Click For Summary
The discussion revolves around a partition theorem that applies to almost all cases, except for a finite number of exceptions. The theorem reportedly involves the number of ways to partition prime numbers, specifically mentioning the numbers 17 or 19, with a result of 237. Participants note that this concept aligns with "almost everywhere" theorems commonly used in number theory, which focus on proving results for nearly all cases despite infinite possibilities. The original poster expresses confusion due to a long memory gap but seeks clarification or identification of the theorem. Additional details or keywords could aid in locating the specific theorem in question.
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.
 
Thread 'How to define a vector field?'
Hello! In one book I saw that function ##V## of 3 variables ##V_x, V_y, V_z## (vector field in 3D) can be decomposed in a Taylor series without higher-order terms (partial derivative of second power and higher) at point ##(0,0,0)## such way: I think so: higher-order terms can be neglected because partial derivative of second power and higher are equal to 0. Is this true? And how to define vector field correctly for this case? (In the book I found nothing and my attempt was wrong...

Similar threads

  • · Replies 3 ·
Replies
3
Views
860
  • · Replies 14 ·
Replies
14
Views
3K
Replies
5
Views
6K
Replies
4
Views
5K
  • · Replies 68 ·
3
Replies
68
Views
12K
  • · Replies 9 ·
Replies
9
Views
2K
  • · Replies 1 ·
Replies
1
Views
3K
  • · Replies 3 ·
Replies
3
Views
2K
Replies
6
Views
2K
  • · Replies 3 ·
Replies
3
Views
1K