TY - JOUR
T1 - The number of nilpotent semigroups of degree 3
AU - Distler, Andreas
AU - D. Mitchell, James
PY - 2012
Y1 - 2012
N2 - A semigroup is \emph{nilpotent} of degree 3 if it has a zero, every product of 3 elements equals the zero, and some product of 2 elements is non-zero. It is part of the folklore of semigroup theory that almost all finite semigroups are nilpotent of degree 3. We give formulae for the number of nilpotent semigroups of degree 3 with $n\in\N$ elements up to equality, isomorphism, and isomorphism or anti-isomorphism. Likewise, we give formulae for the number of nilpotent commutative semigroups with $n$ elements up to equality and up to isomorphism.
AB - A semigroup is \emph{nilpotent} of degree 3 if it has a zero, every product of 3 elements equals the zero, and some product of 2 elements is non-zero. It is part of the folklore of semigroup theory that almost all finite semigroups are nilpotent of degree 3. We give formulae for the number of nilpotent semigroups of degree 3 with $n\in\N$ elements up to equality, isomorphism, and isomorphism or anti-isomorphism. Likewise, we give formulae for the number of nilpotent commutative semigroups with $n$ elements up to equality and up to isomorphism.
UR - http://www.combinatorics.org/ojs/index.php/eljc/article/view/v19i2p51
M3 - Article
SN - 1077-8926
VL - 19
JO - Electronic Journal of Combinatorics
JF - Electronic Journal of Combinatorics
IS - 2
M1 - P51
ER -