  The minimal excludant (mex) of a partition was introduced by Grabner and
Knopfmacher under the name `least gap' and was revived by a couple of papers
due to Andrews and Newman. It has been widely studied in recent years together
with the complementary partition statistic maximal excludant (maex), first
introduced by Chern. Among such recent works, the first and second authors
along with Maji introduced and studied the $r$-chain minimal excludants
(r-chain mex) which led to a new generalization of Euler's classical partition
theorem and the sum-of-mex identity of Andrews and Newman. In this paper, we
first give combinatorial proofs for these two results on r-chain mex. Then we
introduce the r-chain maximal excludants (r-chain maex) and establish the
associated identity for the sum of r-chain maex over all partitions, both
analytically and combinatorially.
