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- Instituto de Astrofísica de CanariasES13 papers
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5 papers · 1 filter
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…
The Casson-Walker-Lescop Invariant and Link Invariants
Jeff Johannes
Formulas previously presented for the Casson-Walker invariant are generalized to Lescop's extension. These formulas in terms of linking numbers and surgery coefficients compute the…