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73 papers · 1 filter
Intrinsically knotted graphs with linklessly embeddable simple minors
Thomas W. Mattman, Ramin Naimi, Andrei Pavelescu +1
It has been an open question whether the deletion or contraction of an edge in an intrinsically knotted graph always yields an intrinsically linked graph. We present a new intrinsi…
New bounds on maximal linkless graphs
Ramin Naimi, Andrei Pavelescu, Elena Pavelescu
We construct a family of maximal linklessly embeddable graphs on vertices and edges for all , and another family on vertices and $m< \frac{25n}{12}-\frac{1}…
On 3-braids and L-space knots
Christine Ruey Shan Lee, Faramarz Vafaee
We classify closed 3-braids which are L-space knots.
Amusing Permutation Representations of Group Extensions
Yongju Bae, J. Scott Carter, Byeorhi Kim
Semi-direct products of finite groups have permutation representations that are constructed from the permutation representations of their constituents. One can envision these in a…
Knot Invariants from Laplacian Matrices
Daniel S. Silver, Susan G. Williams
A checkerboard graph of a special diagram of an oriented link is made a directed, edge-weighted graph in a natural way so that a principal minor of its Laplacian matrix is a Seifer…
Stability and triviality of the transverse invariant from Khovanov homology
Diana Hubbard, Christine Ruey Shan Lee
We explore properties of braids such as their fractional Dehn twist coefficients, right-veeringness, and quasipositivity, in relation to the transverse invariant from Khovanov homo…