5 papers
Optimal Packings of 22 and 33 Unit Squares in a Square
Wolfram Bentz
Let be the side length of the smallest square into which non-overlapping unit squares can be packed. In 2010, the author showed that and . Together wi…
Congruences on Direct Products of Transformation and Matrix Monoids
João Araújo, Wolfram Bentz, Gracinda Gomes
Malcev described the congruences of the monoid of all full transformations on a finite set . Since then, congruences have been characterized in various ot…
Finite Abelian algebras are fully dualizable
Wolfram Bentz, Pierre Gillibert, Luís Sequeira
We show that every finite Abelian algebra A from congruence-permutable varieties admits a full duality. In the process, we prove that A also allows a strong duality, and that the d…
The modularity conjecture holds for linear idempotent varieties
Wolfram Bentz, Luis Sequeira
The "Modularity Conjecture" is the assertion that the join of two nonmodular varieties is nonmodular. We establish the veracity of this conjecture for the case of linear idempotent…
Dualizability of automatic algebras
Wolfram Bentz, Brian A. Davey, Jane G. Pitkethly +1
We make a start on one of George McNulty's Dozen Easy Problems: "Which finite automatic algebras are dualizable?" We give some necessary and some sufficient conditions for dualizab…