Monoid varieties and semigroup theory form a vibrant subfield of algebra that studies classes of algebraic structures defined by equational identities. Monoids, which are semigroups with an identity ...

Semigroup theory examines algebraic structures consisting of a set endowed with an associative binary operation. These structures encompass a wide range of mathematical entities including monoids, ...

We define the notion of the Fourier transform for the rook monoid (also called the symmetric inverse semigroup) and provide two efficient divideand-conquer algorithms (fast Fourier transforms, or FFTs ...