scholarly journals A SHARP UPPER BOUND FOR REGION UNKNOTTING NUMBER OF TORUS KNOTS

2013 ◽  
Vol 22 (05) ◽  
pp. 1350019 ◽  
Author(s):  
SIWACH VIKASH ◽  
MADETI PRABHAKAR
Keyword(s):  
Large Class ◽  
Upper Bound ◽  
Torus Knots ◽  
Torus Links

Region crossing change for a knot or a proper link is an unknotting operation. In this paper, we provide a sharp upper bound on the region unknotting number for a large class of torus knots and proper links. Also, we discuss conditions on torus links to be proper.

Incoherent nullification of torus knots and links

2019 ◽  
Vol 28 (05) ◽  
pp. 1950033
Author(s):  
Zac Bettersworth ◽  
Claus Ernst
Keyword(s):  
Upper Bound ◽  
Torus Knots ◽  
Number Formula ◽  
Knots And Links

In the paper, we study the incoherent nullification number [Formula: see text] of knots and links. We establish an upper bound on the incoherent nullification number of torus knots and links and conjecture that this upper bound is the actual incoherent nullification number of this family. Finally, we establish the actual incoherent nullification number of particular subfamilies of torus knots and links.

On the braid index of links with nested diagrams

1992 ◽  
Vol 111 (2) ◽  
pp. 273-281 ◽  
Author(s):  
D. A. Chalcraft
Keyword(s):  
Lower Bound ◽  
Large Class ◽  
Upper Bound ◽  
Simple Criterion ◽  
Braid Index

AbstractThe number of Seifert circuits in a diagram of a link is well known 9 to be an upper bound for the braid index of the link. The -breadth of the so-called P-polynomial 3 of the link is known 5, 2 to give a lower bound. In this paper we consider a large class of links diagrams, including all diagrams where the interior of every Seifert circuit is empty. We show that either these bounds coincide, or else the upper bound is not sharp, and we obtain a very simple criterion for distinguishing these cases.

scholarly journals Finite n-quandles of torus and two-bridge links

2019 ◽  
Vol 28 (03) ◽  
pp. 1950028
Author(s):  
Alissa S. Crans ◽  
Blake Mellor ◽  
Patrick D. Shanahan ◽  
Jim Hoste
Keyword(s):  
Automorphism Groups ◽  
Cayley Graphs ◽  
Torus Knots ◽  
Knots And Links ◽  
Torus Links

We compute Cayley graphs and automorphism groups for all finite [Formula: see text]-quandles of two-bridge and torus knots and links, as well as torus links with an axis.

THE HOMFLY POLYNOMIAL FOR TORUS LINKS FROM CHERN–SIMONS GAUGE THEORY

1995 ◽  
Vol 10 (07) ◽  
pp. 1045-1089 ◽  
Author(s):  
J. M. F. LABASTIDA ◽  
M. MARIÑO
Keyword(s):  
Gauge Theory ◽  
Gauge Group ◽  
Homfly Polynomial ◽  
Fundamental Representation ◽  
Torus Knots ◽  
Polynomial Invariants ◽  
Chern Simons ◽  
Knots And Links ◽  
Torus Links

Polynomial invariants corresponding to the fundamental representation of the gauge group SU(N) are computed for arbitrary torus knots and links in the framework of Chern–Simons gauge theory making use of knot operators. As a result, a formula for the HOMFLY polynomial for arbitrary torus links is presented.

scholarly journals Subnomality in soluble minimax groups

1974 ◽  
Vol 17 (1) ◽  
pp. 113-128 ◽  
Author(s):  
D. J. McCaughan
Keyword(s):  
Large Class ◽  
Upper Bound ◽  
Nilpotent Groups ◽  
Subnormal Subgroup ◽  
Wreath Products ◽  
Minimal Length ◽  
Intersection Property ◽  
Finite Chain ◽  
Subnormal Subgroups

A subgroup H of a group G is said to be subnormal in G if there is a finite chain of subgroups, each normal in its successor, connecting H to G. If such chains exist there is one of minimal length; the number of strict inclusions in this chain is called the subnormal index, or defect, of H in G. The rather large class of groups which have an upper bound for the subnormal indices of their subnormal subgroups has been inverstigated to same extent, mainly with a restriction to solublegroups — for instance, in [10] McDougall considered soluble p-groups in this class. Robinson, in [14], restricted his attention to wreath products of nilpotent groups but extended his investigations to the strictly larger class of groups in which the intersection of any family of subnormal subgroups is a subnormal subgroup. These groups are said to have the subnormal intersection property.

scholarly journals Knots with propretyR+

1983 ◽  
Vol 6 (3) ◽  
pp. 511-519
Author(s):  
Bradd Evans Clark
Keyword(s):  
Upper Bound ◽  
Connected Sum ◽  
Torus Knots ◽  
Heegaard Genus ◽  
High Tunnel ◽  
Tunnel Number

If we consider the set of manifolds that can be obtained by surgery on a fixed knotK, then we have an associated set of numbers corresponding to the Heegaard genus of these manifolds. It is known that there is an upper bound to this set of numbers. A knotKis said to have PropertyR+if longitudinal surgery yields a manifold of highest possible Heegaard genus among those obtainable by surgery onK. In this paper we show that torus knots,2-bridge knots, and knots which are the connected sum of arbitrarily many(2,m)-torus knots have PropertyR+It is shown that ifKis constructed from the tangles(B1,t1),(B2,t2),…,(Bn,tn)thenT(K)≤1+∑i=1nT(Bi,ti)whereT(K)is the tunnel ofKandT(Bi,ti)is the tunnel number of the tangle(Bi,ti). We show that there exist prime knots of arbitrarily high tunnel number that have PropertyR+and that manifolds of arbitrarily high Heegaard genus can be obtained by surgery on prime knots.

scholarly journals SUPERBRIDGE INDEX OF COMPOSITE KNOTS

2000 ◽  
Vol 09 (05) ◽  
pp. 669-682
Author(s):  
GYO TAEK JIN
Keyword(s):  
Upper Bound ◽  
Connected Sum ◽  
Torus Knots ◽  
Braid Index ◽  
The Difference

An upper bound of the superbridge index of the connected sum of two knots is given in terms of the braid index of the summands. Using this upper bound and minimal polygonal presentations, we give an upper bound in terms of the superbridge index and the bridge index of the summands when they are torus knots. In contrast to the fact that the difference between the sum of bridge indices of two knots and the bridge index of their connected sum is always one, the corresponding difference for the superbridge index can be arbitrarily large.

scholarly journals Upper Bounds for Online Ramsey Games in Random Graphs

2009 ◽  
Vol 18 (1-2) ◽  
pp. 259-270 ◽  
Author(s):  
MARTIN MARCINISZYN ◽  
RETO SPÖHEL ◽  
ANGELIKA STEGER
Keyword(s):  
Large Class ◽  
Lower Bounds ◽  
Random Graphs ◽  
Upper Bound ◽  
Upper Bounds ◽  
Arbitrary Size ◽  
Threshold Functions ◽  
Current Graph ◽  
Player Game ◽  
Monochromatic Copy

Consider the following one-player game. Starting with the empty graph onnvertices, in every step a new edge is drawn uniformly at random and inserted into the current graph. This edge has to be coloured immediately with one ofravailable colours. The player's goal is to avoid creating a monochromatic copy of some fixed graphFfor as long as possible. We prove an upper bound on the typical duration of this game ifFis from a large class of graphs including cliques and cycles of arbitrary size. Together with lower bounds published elsewhere, explicit threshold functions follow.

scholarly journals Lissajous-toric knots

2020 ◽  
Vol 29 (01) ◽  
pp. 2050003
Author(s):  
Marc Soret ◽  
Marina Ville
Keyword(s):  
Upper Bound ◽  
Representation Formula ◽  
Vertical Axis ◽  
Torus Knots ◽  
Torus Knot ◽  
Vertical Circle

A point in the [Formula: see text]-torus knot in [Formula: see text] goes [Formula: see text] times along a vertical circle while this circle rotates [Formula: see text] times around the vertical axis. In the Lissajous-toric knot [Formula: see text], the point goes along a vertical Lissajous curve (parametrized by [Formula: see text] while this curve rotates [Formula: see text] times around the vertical axis. Such a knot has a natural braid representation [Formula: see text] which we investigate here. If [Formula: see text], [Formula: see text] is ribbon; if [Formula: see text], [Formula: see text] is the [Formula: see text]th power of a braid which closes in a ribbon knot. We give an upper bound for the [Formula: see text]-genus of [Formula: see text] in the spirit of the genus of torus knots; we also give examples of [Formula: see text]’s which are trivial knots.

scholarly journals Expected number of locally maximal solutions for random Boolean CSPs

2007 ◽  
Vol DMTCS Proceedings vol. AH,... (Proceedings) ◽  
Author(s):  
Nadia Creignou ◽  
Hervé Daudé ◽  
Olivier Dubois
Keyword(s):  
Large Class ◽  
Constraint Satisfaction ◽  
Upper Bound ◽  
Constraint Satisfaction Problems ◽  
Expected Number ◽  
Exponential Order ◽  
Maximal Solutions ◽  
International Audience ◽  
Locally Maximal ◽  
General Tool

International audience For a large number of random Boolean constraint satisfaction problems, such as random $k$-SAT, we study how the number of locally maximal solutions evolves when constraints are added. We give the exponential order of the expected number of these distinguished solutions and prove it depends on the sensitivity of the allowed constraint functions only. As a by-product we provide a general tool for computing an upper bound of the satisfiability threshold for any problem of a large class of random Boolean CSPs.

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