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Basis Partitions and Their Signature
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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.
SIGMA (Symmetry, Integrability and Geometry: Methods and Application)
Title: Basis Partitions and Their Signature
Description:
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.
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