Nonrational, nonsimple convex polytopes in symplectic geometry.
Nontiles and nonfacets for the Euclidean space, spherical complexes and convex polytopes.
Nonuniqueness Results for X-Ray Problems with Point Sources.
Normal polytopes, triangulations, and Koszul algebras.
Note on a Conjecture of Sierksma.
Note on Bessaga-Klee classification
We collect several variants of the proof of the third case of the Bessaga-Klee relative classification of closed convex bodies in topological vector spaces. We were motivated by the fact that we have not found anywhere in the literature a complete correct proof. In particular, we point out an error in the proof given in the book of C. Bessaga and A. Pełczyński (1975). We further provide a simplified version of T. Dobrowolski's proof of the smooth classification of smooth convex bodies in Banach...
Note on certain partitions of points in
Note on extremal points
Note On H-Convex Functions
Note on H-convex functions.
Note on Lattice-Point-Free Convex Bodies.
Note on Packing of 19 Equal Circles on a Sphere.
Note on Petri and Hamiltonian cycles in cubic polyhedral graphs.
Note on Petrie and Hamiltonian cycles in cubic polyhedral graphs
In this note we show that deciding the existence of a Hamiltonian cycle in a cubic plane graph is equivalent to the problem of the existence of an associated cubic plane multi-3-gonal graph with a Hamiltonian cycle which takes alternately left and right edges at each successive vertex, i.ei̇t is also a Petrie cycle. The Petrie Hamiltonian cycle in an -vertex plane cubic graph can be recognized by an -algorithm.
Note on separation of convex sets
Note on the weight of paths in plane triangulations of minimum degree 4 and 5
The weight of a path in a graph is defined to be the sum of degrees of its vertices in entire graph. It is proved that each plane triangulation of minimum degree 5 contains a path P₅ on 5 vertices of weight at most 29, the bound being precise, and each plane triangulation of minimum degree 4 contains a path P₄ on 4 vertices of weight at most 31.
Note to a paper of Bambah, Rogers and Zassenhaus
Notes on the algebra and geometry of polynomial representations.
Notes on the integral geometry in the hyperbolic plane
Notes on the roots of Steiner polynomials.