Basis Partitions and Their Signature

Krishnaswami Alladi

Department of Mathematics, University of Florida, Gainesville, FL 32611-8105, USA

Аннотация: 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.

Ключевые слова: basis partitions, Rogers–Ramanujan partitions, Durfee squares, sliding operation, signature, partial theta series.

MSC: 05A17, 05A19, 05A15

Поступила: 23 июля 2025 г.; в окончательном варианте 28 ноября 2025 г.; опубликована 11 декабря 2025 г.

Язык публикации: английский

DOI: 10.3842/SIGMA.2025.104

ArXiv: 2507.14734