Geodesic
Staircases to analytic sum-sides for many new integer partition identities of Rogers-Ramanujan type
Shashank Kanade1 ; Matthew C. Russell2
1University of Denver
2Rutgers, The State University of New Jersey
The electronic journal of combinatorics, Tome 26 (2019) no. 1
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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.
DOI : 10.37236/7847
Classification : 05A15, 05A17, 11P84, 17B69

Shashank Kanade  1   ; Matthew C. Russell  2

1 University of Denver
2 Rutgers, The State University of New Jersey 
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Shashank Kanade; Matthew C. Russell. Staircases to analytic sum-sides for many new integer partition identities of Rogers-Ramanujan type. The electronic journal of combinatorics, Tome 26 (2019) no. 1. doi: 10.37236/7847

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