Statistics on some classes of knot shadows

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.

arXiv comment37 pages, 27 figures, 20 tables; added new OEIS entries, closed form for the generating polynomials