4 citations · 15 across the 7 of their papers we have counts for
6 papers · 1 filter
Knot Mosaics with Corner Connection Tiles
Aaron Heap, Una Donovan, Riley Grossman +4
A knot mosaic is a representation of a knot or link on a square grid using a collection of tiles that are either blank or contain a portion of the knot diagram. Traditionally, a pi…
Tabulating Knot Mosaics: Crossing Number 10 or Less
Aaron Heap, Douglas Baldwin, James Canning +1
The study of knot mosaics is based upon representing knot diagrams using a set of tiles on a square grid. This branch of knot theory has many unanswered questions, especially regar…
Space-Efficient Prime Knot 7-Mosaics
Aaron Heap, Natalie LaCourt
The concepts of tile number and space-efficiency for knot mosaics were first explored by Heap and Knowles (arXiv:1702.06462), where they determined the possible tile numbers and sp…
Space-Efficient Knot Mosaics for Prime Knots with Mosaic Number 6
Aaron Heap, Douglas Knowles
In 2008, Kauffman and Lomonaco introduce the concepts of a knot mosaic and the mosaic number of a knot or link, the smallest integer such that a knot or link can be represented…
Tile Number and Space-Efficient Knot Mosaics
Aaron Heap, Douglas Knowles
In this paper we introduce the concept of a space-efficient knot mosaic. That is, we seek to determine how to create knot mosaics using the least number of non-blank tiles necessar…
Bordism Invariants of the Mapping Class Group
Aaron Heap
We define new bordism and spin bordism invariants of certain subgroups of the mapping class group of a surface. In particular, they are invariants of the Johnson filtration of the…