A Stanley–Elder theorem on Cranks and Frobenius symbols

The Stanley–Elder theorem asserts that the number of j’s in the partitions of n is equal to the number of parts that appear at least j times in a given partition of n, summed over all partitions of n. In this paper, we prove that the number of partitions of n with crank > j equals to half the total number of j’s in the Frobenius symbols for n.

This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/10.1007/s40993-021-00285-7

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Work Title A Stanley–Elder theorem on Cranks and Frobenius symbols
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Open Access
Creators
  1. George E. Andrews
  2. Manosij G. Dastidar
  3. Thomas Morrill
Keyword
  1. Partitions
  2. Cranks
  3. Frobenius symbols
  4. Durfee squares
License In Copyright (Rights Reserved)
Work Type Article
Publisher
  1. Research in Number Theory
Publication Date August 18, 2021
Publisher Identifier (DOI)
  1. https://doi.org/10.1007/s40993-021-00285-7
Deposited August 03, 2022

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Version 1
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  • Created
  • Added A-Stanley-Elder-theorem.pdf
  • Added Creator George E. Andrews
  • Added Creator Manosij G. Dastidar
  • Added Creator Thomas Morrill
  • Published
  • Updated Keyword, Publisher's Statement Show Changes
    Keyword
    • Partitions, Cranks, Frobenius symbols, Durfee squares
    Publisher's Statement
    • his version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/10.1007/s40993-021-00285-7
    • This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/10.1007/s40993-021-00285-7
  • Updated