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A unifying combinatorial approach to refined little G\'ollnitz and Capparelli's companion identities
- Source :
- Adv. Appl. Math. 98 (2018): 127-154
- Publication Year :
- 2016
-
Abstract
- Berkovich-Uncu have recently proved a companion of the well-known Capparelli's identities as well as refinements of Savage-Sills' new little G\"ollnitz 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.<br />Comment: This is the second revision submitted to JCTA in June, comments are welcome
- Subjects :
- Mathematics - Combinatorics
Subjects
Details
- Database :
- arXiv
- Journal :
- Adv. Appl. Math. 98 (2018): 127-154
- Publication Type :
- Report
- Accession number :
- edsarx.1603.07068
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1016/j.aam.2018.03.005