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math.GN2000
Operators Extending (Pseudo-)Metrics
Oleg Pikhurko
We introduce a general method of extending (pseudo-)metrics from X to FX, where F is a normal functor on the category of metrizable compacta. For many concrete instances of F, our…
math.CO2000
Lattice Points inside Lattice Polytopes
Oleg Pikhurko
We show that, if the interior of a lattice d-polytope P contains at least one lattice point, then it contains a lattice point whose coefficient of asymmetry with respect to P is at…
math.CO2000
Foata's Bijection for Tree-Like Structures
Oleg Pikhurko
We present bijections enumerating (k,m)-trees, k-gon trees, edge labelled (2,1)-trees, and other tree-like structures. Our constructions are based on Foata's (1971) bijection for c…