2 papers
math.GT2026
An infinite family of knots whose hexagonal mosaic number is only realized in non-reduced projections
Hugh Howards, Jiong Li, Xiaotian Liu +1
We give an infinite family of knots such that for any given , the family contains a knot which can be embedded on a hexagonal -mosaic, but cannot fit on a hexagonal $r…
math.GT2024
Bounding Crossing Number in Rectangular and Hexagonal Knot Mosaics
Hugh Howards, Jiong Li, Xiaotian Liu
Howards and Kobin give a sharp upper bound for crossing number of knots on rectangular mosaics. Here we extend the proof to create a new bound for hexagonal mosaics in all three na…