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Partitions with difference conditions and Alder's conjecture.

Ae Ja Yee1

  • 1Department of Mathematics, Pennsylvania State University, University Park, PA 16802, USA. yee@math.psu.edu

Proceedings of the National Academy of Sciences of the United States of America
|November 18, 2004
PubMed
Summary

Alder

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Area of Science:

  • Number theory
  • Combinatorics
  • Partition theory

Background:

  • Alder's partition conjecture (1956) relates two types of integer partitions.
  • Andrews proved the conjecture for specific cases (d=2r-1, r>=4) in 1971.

Purpose of the Study:

  • To prove Alder's partition conjecture for a broader range of d.
  • To extend the findings of Andrews' 1971 proof.

Main Methods:

  • The study outlines a proof strategy for Alder's conjecture.
  • The proof applies to partitions with parts differing by at least d.

Main Results:

  • The paper sketches a proof of Alder's conjecture.
  • The proof is valid for all d >= 32.

Conclusions:

  • Alder's partition conjecture is proven for d >= 32.
  • This work generalizes previous results in partition theory.

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