In Kiselman's semigroup K_n, left zero-cancellation holds for y generated by a2..an but not a1, the solution set to xa1=f has size 1+|K_{n-1}|, and |K_m| is even for odd m and odd for even m.
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Zero Cancellation and Equation Structure in Kiselman's Semigroup
In Kiselman's semigroup K_n, left zero-cancellation holds for y generated by a2..an but not a1, the solution set to xa1=f has size 1+|K_{n-1}|, and |K_m| is even for odd m and odd for even m.