Arithmetic properties and asymptotic formulae for ${\sigma }_o\text{mex}(n)$ and ${\sigma }_e\text{mex}(n)$

Gurinder Singh, Rupam Barman

The minimal excludant of an integer partition is the least positive integer missing from the partition. Let ${\sigma }_o\text{mex}(n)$ (resp., ${\sigma }_e\text{mex}(n)$) denote the sum of odd (re…