Year: 2025
Type: article
Abstract: Basis partitions are minimal partitions corresponding to successive rank vectors. We show combinatorially how basis partitions can be generated from primary partitions which are equivalent to the Rogers-Ramanujan partitions. This leads to the definition of a signature of a basis partition that we use to explain certain parity results. We then study a special class of basis partitions which we term as complete. Finally, we discuss basis partitions and minimal basis partitions among partitions with non-repeating odd parts by representing them using 2-modular graphs.
Author: Krishnaswami Alladi
Institution: University of Florida
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
Funder: Pennsylvania State University
OpenAlex ID: W4417248556
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