Related papers: Generating links that are both quasi-alternating a…
We give an upper bound on the z-degree of the Kauffman polynomial of a link, using bridges of length greater than one which are separated in some tangle decomposition of a link diagram. We construct some examples by wiring together rational…
A virtual link diagram is called {\em (mod $m$) almost classical} if it admits a (mod $m$) Alexander numbering. In \cite{BodenGaudreauHarperNicasWhite}, it is shown that Alexander polynomial for almost classical links can be defined by…
Any directed graph $D=(V(D),A(D))$ in this work is assumed to be finite and without self-loops. A source in a directed graph is a vertex having at least one ingoing arc. A quasi-kernel $Q\subseteq V(D)$ is an independent set in $D$ such…
A rational link may be represented by any of the (infinitely) many link diagrams corresponding to various continued fraction expansions of the same rational number. The continued fraction expansion of the rational number in which all signs…
We prove two approximations of the open problem of whether the adjoint group of a non-nilpotent nil ring can be finitely generated: We show that the adjoint group of a non-nilpotent Jacobson radical cannot be boundedly generated, and on the…
We show that the volume of any Montesinos link can be bounded above and below in terms of the combinatorics of its diagram. This was known for Montesinos links with at most two tangles, and those with at least five tangles. We complete the…
For arborescent links, we present an efficient method of computing their Alexander polynomials. Applying this method, we express the Alexander polynomials of Montesinos links in terms of certain functions associated to rational tangles…
We show a combinatorial argument in the diagram of large class of links, including satellite and hyperbolic links, where for each of which the tunnel number is the minimum possible, the number of its components minus one.
We construct an uncountable family of well-quasi-ordered permutation classes, each with a distinct enumeration sequence. This disproves a conjecture that all well-quasi-ordered permutation classes have algebraic generating functions, and in…
We prove relative versions of many earlier results about almost invariant sets and splittings of groups. In particular, we prove a relative version of the algebraic torus theorem, and we prove the existence and uniqueness of relative…
We built some congruences on semigroups, from where a decomposition of quasi-separative semigroups was obtained.
Let $ D=(V,E) $ be a (possibly infinite) digraph and $ A,B\subseteq V $. A hindrance consists of an $ AB $-separator $ S $ together with a set of disjoint $ AS $-paths linking a proper subset of $ A $ onto $ S $. Hindrances and…
We investigate which plane curves admit rational families of quasi-toric relations. This extends previous results of Takahashi and Tokunaga in the positive case and of the author in the negative case.
In this paper, we study the parallelism between perfect numbers and Leinster groups and continue it by introducing the new concepts of almost and quasi Leinster groups which parallel almost and quasi perfect numbers. These are small…
This paper introduces the concept of Conjectural Link for Complex Networks, in particular, social networks. Conjectural Link we understand as an implicit link, not available in the network, but supposed to be present, based on the…
Recently, Merino extended the classical relation between the $2n$-th Fibonacci number and the number of spanning trees of the $n$-fan graph to ribbon graphs, and established a relation between the $n$-associated Mersenne number and the…
The main results of this paper are generalizations some classical theorems about transversals for families of finite sets to some cases of families of infinite sets.
A Gauss diagram is a simple, combinatorial way to present a knot. It is known that any Vassiliev invariant may be obtained from a Gauss diagram formula that involves counting (with signs and multiplicities) subdiagrams of certain…
We show that doubling, linearly connected metric spaces are quasi-arc connected. This gives a new and short proof of a theorem of Tukia.
We establish a characterization of alternating links in terms of definite spanning surfaces. We apply it to obtain a new proof of Tait's conjecture that reduced alternating diagrams of the same link have the same crossing number and writhe.…