The second minimal excludant and mex sequences (Q6635533)

The minimal excludant (mex) of an integer partition, a concept prominently explored by \textit{G. E. Andrews} and \textit{D. Newman} [Ann. Comb. 23, No. 2, 249--254 (2019; Zbl 1458.11011)] in combinatorial studies, refers to the smallest positive integer not included in the partition. In this paper, the authors introduced the concept of second minimal excludant of an integer partition and analyze its relationship with the minimal excludant. This development leads to the introduction of the mex sequence, from which they derive two elegant identities concerning the number of partitions with a mex sequence of length at least \( r \).