Sum_{k=0n} p(k) where p(k) = number of partitions of k

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SUMMARY

The discussion centers on the mathematical concept of generating functions, specifically in relation to the partition function p(k), which counts the number of ways to express an integer k as a sum of positive integers. The user seeks guidance on creating generating functions and identifying self-similar patterns within polynomials related to partitions. A zipped attachment containing a .doc and .xls file is referenced, which outlines the foundational concepts and provides a generating function for further exploration.

PREREQUISITES
  • Understanding of generating functions in combinatorics
  • Familiarity with the partition function p(k)
  • Basic knowledge of polynomial functions
  • Ability to analyze mathematical patterns and sequences
NEXT STEPS
  • Research the properties of the partition function p(k) in detail
  • Learn how to construct generating functions for various sequences
  • Explore self-similar patterns in mathematical sequences
  • Examine the application of generating functions in combinatorial proofs
USEFUL FOR

Mathematicians, students of combinatorics, and anyone interested in understanding generating functions and partition theory.

ozymandius5
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Very much a beginner in maths and broadening my horizons. I have a series of polynomials that I was hoping to get some insight into, specifically where to beginning looking re. a method of creating a generating function, as well as some self similar patterns and links that explain them. Any help would be greatly appreciated.

I think the zipped .doc and .xls attachment lays out the broad strokes.
 

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If you haven't done so, take a look at this page. Among other things that might interest you, a generating function is provided there.

EDIT: Considering the thread title is an exact copy of the title of the series in the link, I guess you have seen it. Dig deeper and you'll find a g.f. :)
 

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