Rahul KumarAffiliation: Indian Institute of Technology Roorkee Title Of Talk: Euler's theorem, and partition classes arising from parity, differences, and repeated smallest parts Abstract: In this talk, we first discuss the famous Euler's partition theorem and introduce new partition functions related to it. Next, we present various classes of partition functions such as those related to the parity of the number of parts, to differences of partition numbers, and to partitions with a repeated smallest part. We establish identities connecting these various classes of partitions. Moreover, we will discuss how these identities help us to extend the Euler's partition theorem. If time permits, we will also present an analogue of Legendre's theorem of the partition-theoretic interpretation of Euler's pentagonal number theorem is also derived. This talk is based on the joint works with George Andrews and Aa Ja Yee, and with Nargish Punia.
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Last update made Tue Mar 17 09:40:07 CDT 2026.
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