# Latebreaking Result Talk

## Christian Jäkel

### Breaking the Barrier: A Computation of the Ninth Dedekind Number

The Dedekind numbers are a fast-growing sequence of integers, which are exceptionally hard to compute. Introduced in 1897 by Richard Dedekind, the nth Dedekind number represents the size of the free distributive lattice with n generators, the number of antichains of subsets of an n-element set, and the number of abstract simplicial complexes with n elements. It is also equal to the number of Boolean functions with n variables, composed only of “and” and “or” operators.

After three decades of being an open problem, I will present my successful approach to compute the ninth Dedekind number in this talk. Inspired by Formal Concept Analysis, I developed complexity reduction techniques to tackle this problem. In addition, I discovered formulas that facilitate the efficient computation on GPUs, resulting in significantly faster runtimes compared to conventional CPU computing.

## CV Christian Jäkel

Christian Jäkel (MSc in Mathematics) is a PhD student at Dresden University of Technology — under the supervision of Prof. Stefan E. Schmidt. His research centers on optimization problems in algebraic structures and their behavior under various product operations. Since 2018, he is working as a software engineer at Faro Technologies Inc., focusing on pattern recognition in 3D point clouds.