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On the Moments of Least $r$-Gaps of Partitions and a Conjecture of Baruah and Talukdar
The minimal excludant or mex of a partition, introduced by Andrews and Newman \cite{AN2019,AN2020}, is the smallest positive integer missing from that partition. Baruah, Bhoria, Eyyunni and Maji \cite{BBEM2023} studied the sum of mex split according to parity, together with its $k$-th moments. Balla
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