The goal of this paper is to tabulate all genus one prime virtual knots having diagrams with≤
5 classical crossings. First, we construct all nonlocal prime knots in the thickened torus T× I …

We enumerate chord diagrams without loops and without both loops and parallel chords.
We show that the former ones describe Hamiltonian paths in $ n $-dimensional …

This paper provides the complete table of prime knot projections with their mirror images,
without redundancy, up to eight double points systematically thorough a finite procedure by …

We present a table of knots in a thickened torus T× I the diagrams of which have less than
five crossing points. The knots are constructed by a three-step process: enumeration of …

Вестник ЮУрГУ. Серия "Математика. Механика. Физика". - 2013. - Т.5, №1 Page 1 . « . .
» 8 515.162.3 , 1 . . 2 T×I, - . ¡ ¢£¤¥¦¤ §¥©: ¤ , § ¤ ¦ § , © © §¥. F×I, F – - , . S3 T×I, T = S1 ×S1 …

Построена таблица узлов в T× I, минимальные диаграммы которых не лежат в кольце и
соответствуют графу «октаэдр». Табулирование проводится в три этапа. Сначала мы …

In this paper we compute the sharp lower bounds for the crossing number of n-string k-loop
essential tangles. For essential tangles with only string components, we characterize the …

We compose the table of knots in the thickened torus T x I having diagrams with at most 4
crossings. The knots are constructed by the three-step process. First we list regular graphs of …

Напомним, что классический узел представляет собой произвольную простую
замкнутую кривую в трёхмерном пространстве R3. При изображении классических …

A knot can be thought of as a knotted piece of string with the ends glued together. A tangle is
formed by intersecting a knot with a 3-dimensional ball. The portion of the knot in the interior …