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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Siladić’s theorem: Weighted words, refinement and companion
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by Jehanne Dousse PDF
Proc. Amer. Math. Soc. 145 (2017), 1997-2009 Request permission


In a previous paper, the author gave a combinatorial proof and refinement of Siladić’s theorem, a Rogers-Ramanujan type partition identity arising from the study of Lie algebras. Here we use the basic idea of the method of weighted words introduced by Alladi and Gordon to give a non-dilated version, further refinement and companion of Siladić’s theorem. However, while in the work of Alladi and Gordon, identities were proved by doing transformations on generating functions, we use recurrences and $q$-difference equations, as the original method seems difficult to apply in our case. As the non-dilated version features the same infinite product as Schur’s theorem, another dilation allows us to find a new interesting companion of Schur’s theorem, with difference conditions very different from the original ones.
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Additional Information
  • Jehanne Dousse
  • Affiliation: Institut für Mathematik, Universitat Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland
  • MR Author ID: 1036858
  • ORCID: 0000-0001-6825-0389
  • Received by editor(s): February 17, 2016
  • Received by editor(s) in revised form: July 12, 2016
  • Published electronically: November 18, 2016
  • Communicated by: Ken Ono
  • © Copyright 2016 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 145 (2017), 1997-2009
  • MSC (2010): Primary 05A17, 11P84
  • DOI:
  • MathSciNet review: 3611315