• Corpus ID: 214743203

Petal Projections, Knot Colorings and Determinants

```@article{Henrich2020PetalPK,
title={Petal Projections, Knot Colorings and Determinants},
author={Allison Henrich and Robert Truax},
journal={arXiv: Geometric Topology},
year={2020}
}```
• Published 31 March 2020
• Mathematics
• arXiv: Geometric Topology
An ubercrossing diagram is a knot diagram with only one crossing that may involve more than two strands of the knot. Such a diagram without any nested loops is called a petal projection. Every knot has a petal projection from which the knot can be recovered using a permutation that represents strand heights. Using this permutation, we give an algorithm that determines the \$p\$-colorability and the determinants of knots from their petal projections. In particular, we compute the determinants of…

References

SHOWING 1-8 OF 8 REFERENCES
A Reidemeister type theorem for petal diagrams of knots
• Mathematics
Topology and its Applications
• 2019
Knot projections with a single multi-crossing
• Mathematics
• 2012
An n-crossing is a singular point in a projection of a link at which n strands cross such that each strand travels straight through the crossing. We introduce the notion of an ubercrossing
Bounds on \"{U}bercrossing and Petal Numbers for Knots
• Mathematics
• 2013
An \$n\$-crossing is a point in the projection of a knot where \$n\$ strands cross so that each strand bisects the crossing. An \"ubercrossing projection has a single \$n\$-crossing and a petal projection
Knot Theory
This project presents some basic concepts and results of knot theory, including important definitions and basic concepts, and develops some combinatorial techniques, including tricolorability and the linking number.
Invariants of Random Knots and Links
• Mathematics
Discret. Comput. Geom.
• 2016
These are the first precise formulas given for the distributions and higher moments of invariants in any model for random knots or links in R3 using the Petaluma model.
The Knot Book
Are you looking to uncover the knot book Digitalbook. Correct here it is possible to locate as well as download the knot book Book. We've got ebooks for every single topic the knot book accessible
The Knot Book. The American Mathematical Society, 2004: 1-16
• ALLISON HENRICH AND ROBIN TRUAX
• 2004
An Interactive Introduction to Knot Theory
• Dover Publications,
• 2017