2 papers
math.PR2026
Balanced affine Motzkin paths: Pearson geometry and global endpoint asymptotics
Alexander Omelchenko
We study endpoint distributions of balanced affine weighted Motzkin paths. In the balanced case, the generating-function equation has Pearson-type characteristic geometry. We show…
math.CO2026
Maps on Surfaces as a Structural Framework for Genus-One Virtual Knot Classification
Alexander Omelchenko
We develop a purely combinatorial framework for the systematic enumeration of knot and link diagrams supported on the thickened torus . Using the theory of maps on sur…