Staircases to Analytic Sum-Sides for Many New Integer Partition Identities of Rogers-Ramanujan Type

  • Shashank Kanade
  • Matthew C. Russell


We utilize the technique of staircases and jagged partitions to provide analytic sum-sides to some old and new partition identities of Rogers-Ramanujan type. Firstly, we conjecture a class of new partition identities related to the principally specialized characters of certain level $2$ modules for the affine Lie algebra $A_9^{(2)}$. Secondly, we provide analytic sum-sides to some earlier conjectures of the authors. Next, we use these analytic sum-sides to discover a number of further generalizations. Lastly, we apply this technique to the well-known Capparelli identities and present analytic sum-sides which we believe to be new. All of the new conjectures presented in this article are supported by a strong mathematical evidence.


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