Results 11  20
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462
On iterated torus knots and transversal knots
 Geom. Topol
"... A knot type is exchange reducible if an arbitrary closed nbraid representative K of K can be changed to a closed braid of minimum braid index nmin(K) by a finite sequence of braid isotopies, exchange moves and ±destabilizations. (See Figure 1). In the manuscript [BW] a transversal knot in the stan ..."
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Cited by 17 (4 self)
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A knot type is exchange reducible if an arbitrary closed nbraid representative K of K can be changed to a closed braid of minimum braid index nmin(K) by a finite sequence of braid isotopies, exchange moves and ±destabilizations. (See Figure 1). In the manuscript [BW] a transversal knot
FREE  A Program For Constrained Approximation By Splines With Free Knots
, 1996
"... In this paper a program for the computation and visualization of univariate splines with free knots is described. For given noisy data, the algorithm delivers a polynomial spline with an optimal knot sequence subject to constraints on derivatives. ..."
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In this paper a program for the computation and visualization of univariate splines with free knots is described. For given noisy data, the algorithm delivers a polynomial spline with an optimal knot sequence subject to constraints on derivatives.
Constrained Approximation By Splines With Free Knots
"... In this paper, a method that combines shape preservation and least squares approximation by splines with free knots is developed. Besides the coefficients of the spline a subset of the knot sequence, the socalled free knots, is included in the optimization process resulting in a nonlinear least squ ..."
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Cited by 4 (0 self)
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In this paper, a method that combines shape preservation and least squares approximation by splines with free knots is developed. Besides the coefficients of the spline a subset of the knot sequence, the socalled free knots, is included in the optimization process resulting in a nonlinear least
Knot graphs
, 2008
"... We consider the equivalence classes of graphs induced by the unsigned versions of the Reidemeister moves on knot diagrams. Any graph which is reducible by some finite sequence of these moves, to a graph with no edges is called a knot graph. We show that the class of knot graphs strictly contains the ..."
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Cited by 2 (0 self)
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We consider the equivalence classes of graphs induced by the unsigned versions of the Reidemeister moves on knot diagrams. Any graph which is reducible by some finite sequence of these moves, to a graph with no edges is called a knot graph. We show that the class of knot graphs strictly contains
CABLING SEQUENCES OF TUNNELS OF TORUS KNOTS
, 812
"... Abstract. In previous work, we developed a theory of tunnels of tunnel number 1 knots in S 3. It yields a parameterization in which each tunnel is described uniquely by a finite sequence of rational parameters and a finite sequence of 0’s and 1’s, that together encode a procedure for constructing th ..."
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Cited by 5 (4 self)
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Abstract. In previous work, we developed a theory of tunnels of tunnel number 1 knots in S 3. It yields a parameterization in which each tunnel is described uniquely by a finite sequence of rational parameters and a finite sequence of 0’s and 1’s, that together encode a procedure for constructing
POLYNOMIAL KNOTS AND MINIMAL DEGREE SEQUENCE
"... Polynomial knots were introduced by Vasiliev and are now studied by many mathematicians. They are important from Algebraic Geometry point of view to settle the famous age old conjucture of Abhyankar. Notion of degree sequence and minimal degree sequence has been introduced to understand the knot ty ..."
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Polynomial knots were introduced by Vasiliev and are now studied by many mathematicians. They are important from Algebraic Geometry point of view to settle the famous age old conjucture of Abhyankar. Notion of degree sequence and minimal degree sequence has been introduced to understand the knot
PLUMBERS ’ KNOTS
, 811
"... We describe a new version of finitecomplexity knot theory in R 3 and we resolve the fundamental questions about enumerating and distinguishing knot types in this theory. We further show that these knot spaces stabilize to a space with the components of the classical knot space, indicating that our ..."
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(long) knots. As such, these spaces provide us with a model for classical knot theory, one application of which will be our construction of an unstable Vassiliev spectral sequence in [3]. We begin by showing that each plumbers ’ curve space Pn admits a cell decomposition
On iterated torus knots and transversal knots
, 2001
"... A knot type is exchange reducible if an arbitrary closed n–braid representative K of K can be changed to a closed braid of minimum braid index nmin(K) by a finite sequence of braid isotopies, exchange moves and ±–destabilizations. (See Figure 1). In the manuscript [6] a transversal knot in the stand ..."
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A knot type is exchange reducible if an arbitrary closed n–braid representative K of K can be changed to a closed braid of minimum braid index nmin(K) by a finite sequence of braid isotopies, exchange moves and ±–destabilizations. (See Figure 1). In the manuscript [6] a transversal knot
On iterated torus knots and transversal knots
, 2001
"... A knot type is exchange reducible if an arbitrary closed n{braid representative K of K can be changed to a closed braid of minimum braid index nmin(K) by a nite sequence of braid isotopies, exchange moves and {destabilizations. (See Figure 1). In the manuscript [6] a transversal knot in the standard ..."
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A knot type is exchange reducible if an arbitrary closed n{braid representative K of K can be changed to a closed braid of minimum braid index nmin(K) by a nite sequence of braid isotopies, exchange moves and {destabilizations. (See Figure 1). In the manuscript [6] a transversal knot
Tie knots, random walks and topology
 PHYSICA A
, 2000
"... Necktie knots are inherently topological structures; what makes them tractable is the particular manner in which they are constructed. This observation motivates a map between tie knots and persistent walks on a triangular lattice. The topological structure embedded in a tie knot may be determined b ..."
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Cited by 3 (0 self)
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by appropriately manipulating its projection; we derive corresponding rules for tie knot sequences. We classify knots according to their size and shape and quantify the number of knots in a class. Aesthetic knots are characterised by the conditions of symmetry and balance. Of the 85 knots which may be tied
Results 11  20
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462