Statistics on some classes of knot shadows

TL;DR

This paper studies the enumeration of state diagrams for specific classes of knot shadows generated recursively, using generating polynomials to solve the counting problem.

Contribution

It introduces a recursive approach and generating polynomial techniques for enumerating certain classes of knot shadows with connected sum operations.

Findings

Enumeration formulas for classes of knot shadows

Use of generating polynomials for counting

Recursive generation methods

Abstract

The present paper is concerned with the enumeration of the state diagrams for some classes of knot shadows endowed with the usual connected sum operation. We focus on shadows that are recursively generated by knot shadows with up to 3 crossings, and for which the enumeration problem is solved with the help of generating polynomials.