Equations in finite semigroups: Explicit enumeration and asymptotics of solution numbers

Christian Krattenthaler, Thomas Müller

We study the number of solutions of the general semigroup equation in one variable, $X^\al=X^\be$, as well as of the system of equations $X^2=X,Y^2=Y,XY=YX$ in $H\wr T_n$, the wr…