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

作者：Fu, Shishuo^*; Zeng, Jiang

来源：Advances in Applied Mathematics, 2018, 98: 127-154.

DOI：10.1016/j.aam.2018.03.005

• Andrews Boulet Stanley partition function
• k-Strict partition
• Little Gollnitz identities
• Capparelli identities

Berkovich-Uncu have recently proved a companion of the well-known Capparelli's identities as well as refinements of Savage-Sills's new little Gollnitz 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.

• 出版日期2018-7
• 单位重庆大学