We prove almost tight bounds on incidences between points and k-dimensional varieties of bounded degree in R. Our main tools are the Polynomial Ham Sandwich Theorem and induction on both the dimension and the number of points.

Developments in the study of logical limit laws for both labelled and unlabelled structures, based on the methods of Compton (1987/1989), are surveyed, and a sandwich theorem is proved for multiplicative systems.

We obtain subordination and superordination preserving properties for the Saigo type generalized fractional differ-integral operator, defined for multivalent functions in the open unit disk. A differential sandwich-type theorem for these multivalent function, and some consequences are also presented.

We study the problem of how to split many point sets in \(\mathbb {R}^d\) into smaller parts using a few (shared) splitting hyperplanes. This is related classical Ham-Sandwich Theorem. provide logarithmic approximation optimal solution greedy algorithm for submodular optimization.

The Borsuk-Ulam theorem is a fundamental result in algebraic topology, with applications to various areas of Mathematics. A classical application of the Borsuk-Ulam theorem is the Ham Sandwich theorem: The volumes of any n compact sets in R can always be simultaneously bisected by an (n− 1)-dimensional hyperplane. In this paper, we demonstrate the equivalence between the Borsuk-Ulam theorem and...