Skip to main content
×
Home
    • Aa
    • Aa

ELEMENTARY PROOFS OF VARIOUS FACTS ABOUT 3-CORES

  • MICHAEL D. HIRSCHHORN (a1) and JAMES A. SELLERS (a2)
Abstract
Abstract

Using elementary means, we derive an explicit formula for a3(n), the number of 3-core partitions of n, in terms of the prime factorization of 3n+1. Based on this result, we are able to prove several infinite families of arithmetic results involving a3(n), one of which specializes to the recent result of Baruah and Berndt which states that, for all n≥0, a3(4n+1)=a3(n).

    • Send article to Kindle

      To send this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      ELEMENTARY PROOFS OF VARIOUS FACTS ABOUT 3-CORES
      Available formats
      ×
      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about sending content to Dropbox.

      ELEMENTARY PROOFS OF VARIOUS FACTS ABOUT 3-CORES
      Available formats
      ×
      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about sending content to Google Drive.

      ELEMENTARY PROOFS OF VARIOUS FACTS ABOUT 3-CORES
      Available formats
      ×
Copyright
Corresponding author
For correspondence; e-mail: sellersj@math.psu.edu
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[1]N. Baruah and B. Berndt , ‘Partition identities and Ramanujans modular equations’, J. Combin. Theory Ser. A 114(6) (2007), 10241045.

[2]J. Borwein and P. Borwein , ‘A cubic counterpart of Jacobi’s identity and the AGM’, Trans. Amer. Math. Soc. 323(2) (1991), 691701.

[3]J. Borwein , P. Borwein and F. Garvan , ‘Some cubic modular identities of Ramanujan’, Trans. Amer. Math. Soc. 343(1) (1994), 3547.

[4]A. Granville and K. Ono , ‘Defect zero p-blocks for finite simple groups’, Trans. Amer. Math. Soc. 348(1) (1996), 331347.

[6]M. Hirschhorn , F. Garvan and J. Borwein , ‘Cubic analogues of the Jacobian theta function θ(z,q)’, Canad. J. Math. 45(4) (1993), 673694.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Keywords: