Monomial ideal

Summary

A monomial ideal is an ideal of a polynomial ring over a field that is generated by monomials. Membership in a monomial ideal is a combinatorial question about exponent vectors, so many invariants of these ideals can be computed by counting. Every ideal can be deformed to a monomial ideal, its ideal of leading terms with respect to a monomial order. This is the bridge from general ideals to combinatorics through Gröbner bases.