Number Theory & Packing Conjectures

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Abstractions that span open problems and local methods in number theory and geometry, including packing and lattice-point conjectures (Ulam's packing conjecture, Kemnitz's conjecture), asymptotic enumeration techniques (analytic combinatorics), and structural or prime-by-prime analysis (local analysis, Iwasawa group).

5 abstractions in this family — domain-specific abstractions that sit near one another in structural-signature space (k-means over structural-signature embeddings). Each is shown with its short description.

• Analytic Combinatorics — Walter Hayman's 1956 paper "A Generalisation of Stirling's Formula" is considered one of the earliest examples of the saddle-point method.
• Iwasawa group — In mathematics, a group is called an Iwasawa group, M-group or modular group if its lattice of subgroups is modular.
• Kemnitz's Conjecture — In additive number theory, Kemnitz's conjecture states that every set of integer lattice points in the plane has a large subset whose centroid is also a lattice point.
• Local Analysis — In algebraic geometry and related areas of mathematics, local analysis is the practice of looking at a problem relative to each prime number p first, and then later trying to integrate the information gained at each prime into a 'global' picture.
• Ulam's packing conjecture — Ulam's packing conjecture, named for Stanisław Ulam, is a conjecture about the highest possible packing density of identical convex solids in three-dimensional Euclidean space.