Rajat.GuptaAffiliation: Indian Institute of Technology Jodhpur, India Title Of Talk: On the kth smallest part of a partition into distinct parts
URLS: Abstract: In this talk, we first review a classic theorem of Uchimura which states that the difference between the sum of the smallest parts of the partitions of $n$ into an odd number of distinct parts and the corresponding sum for an even number of distinct parts is equal to the number of divisors of $n$. Then we introduce the notion of $k$-th smallest part of a partition of $n$, $s_k(\pi)$ and extend the Uchimura's result. This is a joint work with Noah Lebowitz-Lockard and Professor Joseph Vandehey.
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Last update made Tue Mar 10 21:28:04 CDT 2026.
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