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 -