34 citations · 42 across the 31 of their papers we have counts for
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Even and odd plane labelled bipartite trees
Yury Kochetkov
Let be the set of all plane labelled bipartite trees with white vertices and black. If the number of vertices is even, then the set is a union of tw…
Plane trees, Shabat-Zapponi polynomials and Julia sets
Yury Kochetkov
A tree, embedded into plane, is a dessin d'enfant and its Belyi function is a polynomial --- Shabat polynomial. The Zapponi form of this polynomial is unique, so we can correspond…
On enumeration of tree-rooted planar cubic maps
Yury Kochetkov
We consider planar cubic maps, i.e. connected cubic graphs imbedded into plane, with marked spanning tree and marked directed edge (not in this tree). The number of such objects wi…
Affine transformations of circle and sphere
Irina Busjatskaja, Yury Kochetkov
A non-degenerate two-dimensional linear operator transforms the unit circle into ellipse. Let be the length of its bigger axis and -- the length of smaller. We can defi…
Affine transformations of the plane and their geometrical properties
Irina Busjatskaja, Yury Kochetkov
In this work, oriented for students with knowledge of basics of linear algebra, we demonstrate, how the use of polar decomposition allows one to understand metric properties of non…