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arXiv · 1603.07068

A unifying combinatorial approach to refined little Göllnitz and Capparelli's companion identities

Shishuo Fu·Jiang Zeng
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Abstract

Berkovich-Uncu have recently proved a companion of the well-known Capparelli's identities as well as refinements of Savage-Sills' new little Göllnitz identities. Noticing the connection between their results and Boulet's earlier four-parameter partition generating functions, we discover a new class of partitions, called $k$-strict partitions, to generalize their results. By applying both horizontal and vertical dissections of Ferrers' diagrams with appropriate labellings, we provide a unified combinatorial treatment of their results and shed more lights on the intriguing conditions of their companion to Capparelli's identities.

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Shishuo Fu, Jiang Zeng. 2017-06-25. A unifying combinatorial approach to refined little Göllnitz and Capparelli's companion identities. https://doi.org/10.1016/j.aam.2018.03.005

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