On multiplicative properties of combinatorial cubes
Ilya D. Shkredov
TL;DR
This paper investigates the multiplicative properties of combinatorial cubes, providing new bounds on their product sets and estimates on their multiplicative energy, advancing understanding of their algebraic structure.
Contribution
It introduces new lower bounds for product sets and upper bounds for multiplicative energy of combinatorial cubes, which were previously less understood.
Findings
Established lower bounds for product sets of combinatorial cubes
Derived non-trivial upper estimates for multiplicative energy
Enhanced understanding of algebraic structure of combinatorial cubes
Abstract
We obtain a series of lower bounds for the product set of combinatorial cubes, as well as some non--trivial upper estimates for the multiplicative energy of such sets.
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Taxonomy
TopicsLimits and Structures in Graph Theory · Graph theory and applications · Graph Labeling and Dimension Problems