Trying to track down a Partition theorem

In summary, the conversation discusses a new theorem in partition theory that involves proving theorems for all but a finite number of cases. The theorem involves the number of ways to partition prime numbers and has a specific number of ways for a certain number of partitioning bins. However, the speaker is confused and cannot remember all the details.
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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?
 
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  • #2
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... .
 
  • #3


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.
 

What is a Partition theorem?

A Partition theorem is a mathematical theorem that relates to the partitioning of a set into smaller subsets. It is commonly used in combinatorics and number theory to solve problems involving partitions of integers or other objects.

What is the history of the Partition theorem?

The Partition theorem was first introduced by the Indian mathematician Srinivasa Ramanujan in the early 20th century. It has since been further developed and studied by many other mathematicians, including G. H. Hardy and George Andrews.

What are some applications of the Partition theorem?

The Partition theorem has various applications in number theory, combinatorics, and theoretical computer science. It is used to solve problems involving integer partitions, such as counting the number of ways to divide a set of objects into smaller subsets. It also has applications in the study of modular forms and elliptic curves.

What are some key concepts related to the Partition theorem?

Some key concepts related to the Partition theorem include partitions, generating functions, and modular forms. A partition is a way of writing a positive integer as a sum of smaller positive integers. Generating functions are used to represent and manipulate partitions, while modular forms are used to study their properties.

Are there any open problems related to the Partition theorem?

Yes, there are still many open problems and conjectures related to the Partition theorem. For example, the famous Ramanujan conjecture, which states the number of partitions of an integer can be approximated by a certain algebraic formula, remains unsolved. Additionally, there are ongoing research efforts to generalize the Partition theorem to higher dimensions and different types of objects.

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