8 citations · 35 across the 13 of their papers we have counts for
13 papers · 1 filter
A polynomial pair invariant of alternating knots and links
Michal Jablonowski
We introduce an invariant of alternating knots and links (called here WRP), namely a pair of integer polynomials associated with their two checkerboard planar graphs from their min…
Minimal generating sets of moves for surfaces immersed in the four-space
Michal Jablonowski
For immersed surfaces in the four-space, we have a generating set of the Swenton--Hughes--Kim--Miller spatial moves that relate singular banded diagrams of ambient isotopic immersi…
Upper and lower bound on delta-crossing number and tabulation of knots
Michal Jablonowski
We will strengthen the known upper and lower bounds on the delta-crossing number of knots in therms of the triple-crossing number. The latter bound turns out to be strong enough to…
Tabulation of knots up to five triple-crossings and moves between oriented diagrams
Michał Jabłonowski
We enumerate and show tables of minimal diagrams for all prime knots up to the triple-crossing number equal to five. We derive a minimal generating set of oriented moves connecting…
Minimal generating set of planar moves for surfaces embedded in the four-space
Michal Jablonowski
We derive a minimal generating set of planar moves for diagrams of surfaces embedded in the four-space. These diagrams appear as the bonded classical unlink diagrams.
Triple-crossing number, the genus of a knot or link and torus knots
Michal Jablonowski
We show that the triple-crossing number of any knot is greater or equal to twice its (canonical) genus and we show an even stronger bound in the case of links. As an application we…
Triple-crossing projections, moves on knots and links and their minimal diagrams
Michal Jablonowski, Lukasz Trojanowski
In this paper we present a systematic method to generate prime knot and prime link minimal triple-point projections, and then classify all classical prime knots and prime links wit…
Independence of Yoshikawa eighth move and a minimal generating set of band moves
Michal Jablonowski
Yoshikawa moves were introduced at least quarter-century ago and are still actively used by researchers. For any marked graph diagram we will define its twisted diagram and its mir…
Minimal hard surface-unlink and classical unlink diagrams
Michal Jablonowski
We describe a method for generating minimal hard prime surface-link diagrams. We extend the known examples of minimal hard prime classical unknot and unlink diagrams up to three co…
Presentations and representations of surface singular braid monoids
Michal Jablonowski
The surface singular braid monoid corresponds to marked graph diagrams of knotted surfaces in braid form. In a quest to resolve linearity problem for this monoid, we will show that…
On a banded link presentation of knotted surfaces
Michal Jablonowski
We will discuss a method for visual presentation of knotted surfaces in the four space, by examining a number and a position of its Morse's critical points. Using this method, we w…
On a surface singular braid monoid
Michal Jablonowski
We introduce a monoid corresponding to knotted surfaces in four space, from its hyperbolic splitting represented by marked diagram in braid like form. It has four types of generato…
Knotted surfaces and equivalencies of their diagrams without triple points
Michal Jablonowski
The singularity set of a generic standard projection to the three space of a closed surface linked in four space, consists of at most three types: double points, triple points or b…