2025/11/19 by David O. H. Cutler, Jonas Karlsson, Cutler, David O. H. +3 · 1 voice
Computer Science · Mathematics · #Computational Geometry and Mesh Generation #Digital Image Processing Techniques #Geometric and Algebraic Topology #math.CO
paper · pdf · doi:10.48550/arxiv.2511.15864
openalex publication_date 2025/11/19 · openalex created_date 2025/11/23 · openalex updated_date 2026/07/28
In the first chapter of their classic book "Concrete Mathematics", Graham, Knuth, and Patashnik consider the maximum number of pieces that can be obtained from a pancake by making n cuts with a knife blade that is straight, or bent into a V, or bent twice into a Z. We extend their work by considering knives, or "cookie-cutters", of even more exotic shapes, including a k-armed V, a chain of k connected line segments, long-legged versions of the letters A, E, H, L, M, T, W, or X, a convex polygon, a circle, a phi, a figure 8, a pentagram, a hexagram, or a lollipop (or qoppa). We also consider "constrained" versions of the long-legged letters A, H, L, T, and X. In most cases we are able to determine the maximum number of pieces, although for the constrained A and the lollipop we can only give bounds.