17 citations · 29 across the 5 of their papers we have counts for
6 papers
Finite type invariants of nanowords and nanophrases
Andrew Gibson, Noboru Ito
Homotopy classes of nanowords and nanophrases are combinatorial generalizations of virtual knots and links. Goussarov, Polyak and Viro defined finite type invariants for virtual kn…
Factorization of homotopies of nanophrases
Andrew Gibson
Homotopy on nanophrases is an equivalence relation defined using some data called a homotopy data triple. We define a product on homotopy data triples. We show that any homotopy da…
Homotopy invariants of Gauss words
Andrew Gibson
By defining combinatorial moves, we can define an equivalence relation on Gauss words called homotopy. In this paper we define a homotopy invariant of Gauss words. We use this to s…
Homotopy invariants of Gauss phrases
Andrew Gibson
Equivalence relations can be defined on Gauss phrases using combinatorial moves. In this paper we consider two closely related equivalence relations on Gauss phrases, homotopy and…
Coverings, composites and cables of virtual strings
Andrew Gibson
A virtual string can be defined as an equivalence class of planar diagrams under certain kinds of diagrammatic moves. Virtual strings are related to virtual knots in that a simple…
On tabulating virtual strings
Andrew Gibson
A virtual string can be defined as a closed curve on a surface modulo certain equivalence relations. Turaev defined several invariants of virtual strings which we use to produce a…