منابع مشابه
Geometrically and diagrammatically maximal knots
The ratio of volume to crossing number of a hyperbolic knot is known to be bounded above by the volume of a regular ideal octahedron, and a similar bound is conjectured for the knot determinant per crossing. We investigate a natural question motivated by these bounds: For which knots are these ratios nearly maximal? We show that many families of alternating knots and links simultaneously maximi...
متن کاملOn Minors of Maximal Determinant Matrices
By an old result of Cohn (1965), a Hadamard matrix of order n has no proper Hadamard submatrix of order m > n/2. We generalize this result to maximal determinant submatrices of Hadamard matrices, and show that an interval of length ∼ n/2 is excluded from the allowable orders. We make a conjecture regarding a lower bound for sums of squares of minors of maximal determinant matrices, and give evi...
متن کامل20 04 the Maximal { − 1 , 1 } - Determinant of Order 15
We study the question of finding the maximal determinant of matrices of odd order with entries ±1. The most general upper bound on the maximal determinant, due to Barba, can only be achieved when the order is the sum of two consecutive squares. It is conjectured that the bound is always attained in such cases. Apart from these, only in orders 3, 7, 9, 11, 17 and 21 has the maximal value been es...
متن کاملLissajous Knots and Knots with Lissajous Projections
Knots in R which may be parameterized by a single cosine function in each coordinate are called Lissajous knots. We show that twist knots are Lissajous knots if and only if their Arf invariants are zero. We further prove that all 2-bridge knots and all (3, q)-torus knots have Lissajous projections.
متن کاملOn iterated torus knots and transversal knots
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 contact structure for S3 is de ned to be transversally simple if it is characterized up to trans...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Tokyo Journal of Mathematics
سال: 2007
ISSN: 0387-3870
DOI: 10.3836/tjm/1184963648