A Strange Partition Theorem Related to the Second Atkin-Garvan Moment
Alexander E. Patkowski
TL;DR
This paper explores a novel smallest parts function connected to the second Atkin-Garvan moment, revealing new identities related to the Andrews spt function and Borwein's theta functions.
Contribution
It introduces a new smallest parts function and uncovers identities linking it to established functions like Andrews' spt and Borwein's theta functions.
Findings
Discovered new identities involving the spt function.
Established a connection between the smallest parts function and the second Atkin-Garvan moment.
Enhanced understanding of theta functions in partition theory.
Abstract
This paper contain results on a strange smallest parts function related to the second Atkin-Garvan moment. Some new identities are discovered in relation to Andrews function as well as one of Borweins' two-dimensional theta functions.
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