Basis partitions and their signature

2025/07/19 by Krishnaswami Alladi, Alladi, Krishnaswami
Mathematics · #05A19 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT) #Primary 05A17 #Secondary 05A15

paper · pdf · doi:10.48550/arxiv.2507.14734

openalex publication_date 2025/07/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Some Observations on Dyson's New Symmetries of Partitions

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