23 citations · 35 across the 8 of their papers we have counts for
9 papers
Strong Embeddings of Regular Graphs with Prescribed Automorphism Groups
Reymond Akpanya, Tom Goertzen, Meike Weiß
A classical theorem of Frucht states that every finite group occurs as the automorphism group of a finite graph. We prove an embedded analogue for regular graphs of arbitrary degre…
Kazhdan-Lusztig Basis and Optimization
Tom Goertzen, Geordie Williamson
We describe a conjectural approach to obtaining canonical bases of the Hecke algebra at via continuous quadratic optimization. We focus on Specht modules and proper con…
Humanity's Last Exam
Long Phan, Alice Gatti, Ziwen Han +1168
Benchmarks are important tools for tracking the rapid advancements in large language model (LLM) capabilities. However, benchmarks are not keeping pace in difficulty: LLMs now achi…
Mathematical Foundations of Interlocking Assemblies
Tom Goertzen
The study of interlocking assemblies is an emerging field with applications in various disciplines. However, to this day, the mathematical treatment of these assemblies has been sp…
Constructing Interlocking Assemblies with Crystallographic Symmetries
Tom Goertzen
This work presents a construction method for interlocking assemblies based on planar crystallographic symmetries. Planar crystallographic groups, also known as wallpaper groups, co…
Topologically Interlocking Blocks inside the Tetroctahedrille
Reymond Akpanya, Tom Goertzen, Alice C. Niemeyer
A topological interlocking assembly consists of rigid blocks together with a fixed frame, such that any subset of blocks is kinematically constrained and therefore cannot be remove…
Mechanical Comparison of Arrangement Strategies for Topological Interlocking Assemblies
Tom Goertzen, Domen Macek, Lukas Schnelle +4
Topological Interlocking assemblies are arrangements of blocks kinematically constrained by a fixed frame, such that all rigid body motions of each block are constrained only by it…
A Framework for Symmetric Self-Intersecting Surfaces
Christian Amend, Tom Goertzen
3D printing of surfaces has become an established method for prototyping and visualisation. However, surfaces often contain certain degenerations, such as self-intersecting faces o…
Surfaces with given Automorphism Group
Reymond Akpanya, Tom Goertzen
Frucht showed that, for any finite group , there exists a cubic graph such that its automorphism group is isomorphic to . For groups generated by two elements we simplify his…