This page will be dedicated to experiments I have been doing with numerical semigroups, for several years…

I am in a position to made public that the number of numerical semigroups with genus 55 is: 1,142,140,736,859

The highest number previously known is for genus 52. It is 266,815,155,103, about a quarter of the number of numerical semigroups of genus 55. It has been computed by Maria Bras-Amorós and appears in an entry of the Neil J. A. Sloane’s On-Line Encyclopedia of Integer Sequences.

The following nice images have been obtained using the number of numerical semigroups by genus and multiplicity. Other related images will be available here…