combinatorial commutative algebra

combinatorial commutative algebra (uncountable)

1. (algebra) 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.
   • 2011, Viviana Ene, Jũrgen Herzog, Gröbner Bases in Commutative Algebra, American Mathematical Society, page 88:

     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.

   • 2013, Aaron N. Siegel, Combinatorial Game Theory, American Mathematical Society, page 269:

     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.

• Algebraic combinatorics on Wikipedia.Wikipedia
• Polyhedral combinatorics on Wikipedia.Wikipedia