Methods of commutative algebra in (enumerative) combinatorics.
A selection of the following topics:

• Stanley-Reisner theory
• Monomial ideals and their resolutions
• Gröbner-bases and generic initial ideals
• Alexander-duality
• Toric ideals and monoid rings
• Hilbert-sieries
• Dimension, depth, Cohen-Macaulay
• local cohomology, canonical module, Gorenstein, duality
• Lefschetz elements, Kähler-package, unimodaliy

[MS] Miller, Sturmfels: Combinatorial Commutative Algebra; Springer GTM 227.
[S] Stanley: Combinatorics an Commutative Algebra; Birkhäuser PM41.
[BG] Bruns, Gubeladze: Polytopes, Rings, and K-Theory; Springer SMM
[AY] Adiprasito, Yashfe: The Partition Complex: an invitation to combinatorial commutative algebra; arXiv:2008.01044 [math.CO]