combinatorial commutative algebra
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English
Noun
combinatorial commutative algebra (uncountable)
- (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.
Translations
discipline in mathematics
Further reading
Algebraic combinatorics on Wikipedia.Wikipedia - Polyhedral combinatorics on Wikipedia.Wikipedia
