Zobrazeno 1 - 10
of 362
pro vyhledávání: '"57K12"'
Autor:
Bardakov, V. G., Iskra, A. L.
The class transposition group $CT(\mathbb{Z})$ was introduced by S. Kohl in 2010. It is a countable subgroup of the permutation group $Sym(\mathbb{Z})$ of the set of integers $\mathbb{Z}$. We study products of two class transpositions $CT(\mathbb{Z})
Externí odkaz:
http://arxiv.org/abs/2409.13341
Autor:
Kauffman, Louis H
This paper discusses a generalization of virtual knot theory that we call multi-virtual knot theory. Multi-virtual knot theory uses a multiplicity of types of virtual crossings. As we will explain, this multiplicity is motivated by the way it arises
Externí odkaz:
http://arxiv.org/abs/2409.07499
In this paper, we extend the theory of planar pseudo knots to the theories of annular and toroidal pseudo knots. Pseudo knots are defined as equivalence classes under Reidemeister-like moves of knot diagrams characterized by crossings with undefined
Externí odkaz:
http://arxiv.org/abs/2409.03537
Autor:
Kindred, Thomas
Gabai proved that any plumbing, or Murasugi sum, of $\pi_1$-essential Seifert surfaces is also $\pi_1$-essential, and Ozawa extended this result to unoriented spanning surfaces. We show that the analogous statement about geometrically essential surfa
Externí odkaz:
http://arxiv.org/abs/2408.16948
We introduce a generalization of the quandle polynomial. We prove that our polynomial is an invariant of stuquandles. Furthermore, we use the invariant of stuquandles to define a polynomial invariant of stuck links. As a byproduct, we obtain a polyno
Externí odkaz:
http://arxiv.org/abs/2408.07695
Autor:
Hatano, Tomoaki, Nozaki, Yuta
For classical knots, it is well known that their determinants mod $8$ are classified by the Arf invariant. Boden and Karimi introduced a determinant of checkerboard colorable virtual knots. We prove that their determinant mod $8$ is classified by the
Externí odkaz:
http://arxiv.org/abs/2408.01891
Autor:
Khesin, Boris, Saldanha, Nicolau C.
We consider domino tilings of 3D cubiculated regions. The tilings have two invariants, flux and twist, often integer-valued, which are given in purely combinatorial terms. These invariants allow one to classify the tilings with respect to certain ele
Externí odkaz:
http://arxiv.org/abs/2408.00522
Autor:
Ceniceros, Jose, Klivans, Max
We enhance the pointed quandle counting invariant of linkoids through the use of quivers analogously to quandle coloring quivers. This allows us to generalize the in-degree polynomial invariant of links to linkoids. Additionally, we introduce a new l
Externí odkaz:
http://arxiv.org/abs/2407.21606
Autor:
Farinati, Marco A.
I propose a notation for biracks that includes from the begining the knowledege of the associated (or underlying, or derived) rack structure. Motivated by results of Rump in the involutive case, this notation allows to generalize some results from in
Externí odkaz:
http://arxiv.org/abs/2407.07650
While knotoids on the sphere are well-understood by a variety of invariants, knotoids on the plane have proven more subtle to classify due to their multitude over knotoids on the sphere and a lack of invariants that detect a diagram's planar nature.
Externí odkaz:
http://arxiv.org/abs/2407.07489