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math.CO2016
Enumeration of Regular Maps on Surfaces of a Given Genus
E. S. Krasko, A. V. Omelchenko
In the present work the rooted and unrooted d-regular maps on 2-dimentional oriented surfaces of genus g are enumerated. Separately and in more detail the case of d-regular maps wi…
math.CO2016
Enumeration of 4-regular one-face maps
Evgeniy Krasko, Alexander Omelchenko
We give explicit formulas enumerating 4-regular labelled and unlabelled one-face maps.
math.CO2016
Enumeration of Chord Diagrams without Loops and Parallel Chords
Evgeniy Krasko, Alexander Omelchenko
We enumerate chord diagrams without loops and without both loops and parallel chords. We show that the former ones describe Hamiltonian paths in -dimensional octahedrons. The la…