Link invariants from finite biracks

Sam Nelson

Banach Center Publications (2014)

  • Volume: 100, Issue: 1, page 197-212
  • ISSN: 0137-6934

Abstract

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A birack is an algebraic structure with axioms encoding the blackboard-framed Reidemeister moves, incorporating quandles, racks, strong biquandles and semiquandles as special cases. In this paper we extend the counting invariant for finite racks to the case of finite biracks. We introduce a family of biracks generalizing Alexander quandles, (t,s)-racks, Alexander biquandles and Silver-Williams switches, known as (τ,σ,ρ)-biracks. We consider enhancements of the counting invariant using writhe vectors, image subbiracks, and birack polynomials.

How to cite

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Sam Nelson. "Link invariants from finite biracks." Banach Center Publications 100.1 (2014): 197-212. <http://eudml.org/doc/282196>.

@article{SamNelson2014,
abstract = {A birack is an algebraic structure with axioms encoding the blackboard-framed Reidemeister moves, incorporating quandles, racks, strong biquandles and semiquandles as special cases. In this paper we extend the counting invariant for finite racks to the case of finite biracks. We introduce a family of biracks generalizing Alexander quandles, (t,s)-racks, Alexander biquandles and Silver-Williams switches, known as (τ,σ,ρ)-biracks. We consider enhancements of the counting invariant using writhe vectors, image subbiracks, and birack polynomials.},
author = {Sam Nelson},
journal = {Banach Center Publications},
keywords = {birack; biquandle; virtual knot; enhancement of counting invariants},
language = {eng},
number = {1},
pages = {197-212},
title = {Link invariants from finite biracks},
url = {http://eudml.org/doc/282196},
volume = {100},
year = {2014},
}

TY - JOUR
AU - Sam Nelson
TI - Link invariants from finite biracks
JO - Banach Center Publications
PY - 2014
VL - 100
IS - 1
SP - 197
EP - 212
AB - A birack is an algebraic structure with axioms encoding the blackboard-framed Reidemeister moves, incorporating quandles, racks, strong biquandles and semiquandles as special cases. In this paper we extend the counting invariant for finite racks to the case of finite biracks. We introduce a family of biracks generalizing Alexander quandles, (t,s)-racks, Alexander biquandles and Silver-Williams switches, known as (τ,σ,ρ)-biracks. We consider enhancements of the counting invariant using writhe vectors, image subbiracks, and birack polynomials.
LA - eng
KW - birack; biquandle; virtual knot; enhancement of counting invariants
UR - http://eudml.org/doc/282196
ER -

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