3 citations · 7 across the 3 of their papers we have counts for
9 papers
Euclidean tetrahedra and knot invariants
I. G. Korepanov
We construct knot invariants on the basis of ascribing Euclidean geometric values to a triangulation of sphere S^3 where the knot lies. The main new feature of this construction co…
Algebraic formulas whose structure imitates Pachner moves and new types of acyclic complexes
Igor G. Korepanov
What discuss the problem of obtaining new manifold invariants via different analogues of 6j-symbols and the torsion of acyclic complexes.
Exact solution for a matrix dynamical system with usual and Hadamard inverses
I. G. Korepanov
Let A be an n*n matrix with entries a_ij in the field C. Consider the following two involutive operations on such matrices: the matrix inversion I: A -> A^-1 and the element-by-ele…
The method of vacuum vectors in the theory of Yang - Baxter equation
I. G. Korepanov
In modern terminology, this is the first published paper where the solutions of Yang - Baxter equation "at roots of unity" were analyzed and shown to be related to algebraic curves…
A formula with hypervolumes of six 4-simplices and two discrete curvatures
I. G. Korepanov
One of the generalizations of the pentagon equation to higher dimensions is the so-called "six-term equation". Geometrically, it corresponds to one of the "Alexander moves", that i…
A formula with volumes of five tetrahedra and discrete curvature
I. G. Korepanov
Given five points in a three-dimensional euclidean space, one can consider five tetrahedra, using those points as vertices. We present a pentagon-like formula containing the produc…