5 papers
Classification of (uncolored) bonded knots and links
BoÅ¡tjan GabrovÅ¡ek, Matic SimoniÄ, Wanda Niemyska
We present a systematic classification of uncolored bonded knots with singularity number at most seven. Bonded knots provide a topological model for closed protein chains with intr…
A table of knotoids in up to seven crossings
Boštjan Gabrovšek, Paolo Cavicchioli
We present a complete classification of spherical knotoids with up to six crossings and conjecture that our classification up to seven crossings is complete. Our work extends the t…
Bonded braids and the Markov theorem
Paolo Cavicchioli, BoÅ¡tjan GabrovÅ¡ek, Matic SimoniÄ
Bonded knots arise naturally in topological protein modeling, where intramolecular interactions such as disulfide bridges stabilize folded configurations. These structures extend c…
Classification of algebraic tangles
Bartosz Ambrozy Gren, Joanna Ida Sulkowska, Boštjan Gabrovšek
We study algebraic tangles as fundamental components in knot theory, developing a systematic approach to classify and tabulate prime tangles using a novel canonical representation.…
The bracket polynomial of bonded knots and applications to entangles proteins
BoÅ¡tjan GabrovÅ¡ek, Matic SimoniÄ
We model proteins with intramolecular bonds, such as disulfide bridges, using the concept of bonded knots -- closed loops in three-dimensional space equipped with additional bonds…