A Kiselman monoid 
is the monoid with generators 
and defining relations 
for 
and 
for 
(D'Andrea and Stella 2026). The generators
are idempotent. For 
, the monoid consists only of
its identity element. The cardinalities
for 
,
1, ... are 1, 2, 5, 18, 115, 1710, 83973, 22263378, ... (OEIS A125625).
For the asymptotic growth of these cardinalities, D'Andrea and Stella (2026) proved that the even- and odd-index limits of 
are distinct. More precisely, their constants
satisfy
 |
D'Andrea and Stella (2026) report using ChatGPT-assisted computations in discovering this separation.
