11 citations · 43 across the 30 of their papers we have counts for
6 papers · 1 filter
On examples of difference operators for -valued functions over finite sets
Oleg Karpenkov
Recently V.I.Arnold have formulated a geometrical concept of monads and apply it to the study of difference operators on the sets of -valued sequences of length . In th…
Approximating reals by rationals of the form a/b^2
Oleg Karpenkov
In this note we formulate some questions in the study of approximations of reals by rationals of the form a/b^2 arising in theory of Shr"odinger equations. We hope to attract atten…
Combinatorics of multiboundary singularities B_n^l and Bernoulli-Euler numbers
Oleg Karpenkov
Consider generalizations of the boundary singularities B_n of the functions on the real line to the case where the boundary consists of a finite number of l points. These singulari…
Elementary notions of lattice trigonometry
Oleg Karpenkov
In this paper we study properties of lattice trigonometric functions of lattice angles in lattice geometry. We introduce the definition of sums of lattice angles and establish a ne…
Classification of lattice-regular lattice convex polytopes
Oleg Karpenkov
In this paper for any dimension n we give a complete list of lattice convex polytopes in R^n that are regular with respect to the group of affine transformations preserving the lat…
Three examples of three-dimensional continued fractions in the sense of Klein
Oleg Karpenkov
The problem of investigation of the simplest n-dimensional continued fraction in the sense of Klein for n>2 was posed by V.Arnold. The answer for the case of n=2 can be found in th…