Meaning of additive combinatorics | Babel Free

Definitions

A subbranch of combinatorics that concerns additive problems expressed using sumsets.

uncountable

Examples

“One major area of study⟳ in additive combinatorics is that of inverse problems: for instance, given the sumset A#43;B is small in size, what can we say⟳ about the structures of A and B? In the case of integer sumsets, Freiman's theorem provides a partial answer⟳.”

“2007, Andrew Granville, Additive Combinatorics, American Mathematical Society, https://books.google.com.au/books?id=SOVPnwEACAAJ&dq=%22Additive+combinatorics%22&hl=en&newbks=1&newbks_redir=0&sa=X&ved=2ahUKEwj5zJbJ0bLsAhUQX30KHTZYAZwQ6AEwRnoECBwQAg.”

“We now discuss⟳ what appears at first glance⟳ to be an unrelated topic, namely that of additive combinatorics (and its noncommutative counterpart, multiplicative combinatorics). One of the main objects of study⟳ in either additive or multiplicative combinatorics are approximate groups — sets A (typically finite) contained in an additive or multiplicative ambient group G that are "almost groups" in the sense⟳ that they are "almost" closed under either addition or multiplication.”

“This book deals with additive combinatorics, a vibrant area of current mathematical research⟳. Additive combinatorics—an offspring of combinatorial number⟳ theory and additive number⟳ theory—can be described as the study⟳ of combinatorial properties of sumsets (collections of sums with terms from given subsets) in additive structures.”

CEFR level