A Random Geometry Game Breaks a Carefully Simplified Set Conjecture
A random point-marking game reveals why one tidy strategy for building set unions without cancellation must fail.
combinatorial geometry
How a Hypercube Ribbon Tamed the Signed-Permutation Polytope
A hidden ribbon in a hypercube’s face structure reveals a cycle through every facet of the more complex B-permutahedron.
Four Runners, One Missing Fraction, and a Map of Their Motion
A complete classification of four-runner distances reveals a rigid fraction sequence, one missing value, and a solitary speed-pattern exception.