It is well known that the minimum crossing number of an alternating link equals the number
of crossings in any reduced alternating link diagram of the link. This remarkable result is an …

A long standing open conjecture states that if a link $\mathcal {K} $ is alternating, then its
ropelength $ L (\mathcal {K}) $ is at least of the order $ O (Cr (\mathcal {K})) $. A recent result …

We provide a combinatorial characterisation of positive diagrams satisfying the equality in
the Morton-Franks-Williams bound for the degrees of the HOMFLY-PT polynomial. This …

Мы применяем инварианты М. Поляка и М. Бранденбурского для получения оценок на
числа перекрёстков (замкнутых) кос и расширяем известные критерии минимальности …

We describe a new class of minimal link diagrams. This class includes certain alternating
diagrams, the standard diagrams of all torus links, and numerous homogeneous diagrams …

The present thesis is devoted to knot theory. We elaborate on recent developments in
polynomial invariants and obtain new applications for complexity measures of knots given …

The thesis is devoted to knot theory. We study diagrams of knots, links, braids, and tangles
with the minimum number of crossings, the minimum number of Seifert circles, and other …