Meaning of combinatorial commutative algebra | Babel Free

Definitions

A relatively new discipline in mathematics that combines techniques and concepts from combinatorics and commutative algebra, and in which the geometry of convex polytopes also plays a significant role.

uncountable

Examples

“This construction has become a fundamental tool in combinatorial commutative algebra due to the work of Stanley, Hochster and Reisner ([Ho77], [S75], [S96], [R76]).”

“2013, Anna M. Bigatti, Philippe Gimenez, Eduardo Sáenz-de-Cabezón Introduction, Anna M. Bigatti, Philippe Gimenez, Eduardo Sáenz-de-Cabezón (editors), Monomial Ideals, Computations and Applications, Springer, page vii, Monomial ideals and algebras are among the simplest structures in commutative algebra and the main objects in combinatorial commutative algebra.”

“Using techniques from combinatorial commutative algebra [MS05, KM], they showed that certain lattice games admit a particular type of algebraic decomposition known as affine stratifications, from which a finitely representable winning strategy can be recovered.”

CEFR level