The Expected Embedding Dimension, type and weight of a Numerical Semigroup
Abstract
We study statistical properties of numerical semigroups of genus g as g goes to infinity. More specifically, we answer a question of Eliahou by showing that as g goes to infinity, the proportion of numerical semigroups of genus g with embedding dimension close to g/5 approaches 1. We prove similar results for the type and weight of a numerical semigroup of genus g.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.