Abstract A triangulation of a polygon has an associated Stanley–Reisner ideal. We obtain full algebraic and combinatorial understanding these ideals describe their separated models. More generally, we do this for stacked simplicial complexes, in particular polytopes.

Let I ⊂ K[x1, . . . , xn] be a zero-dimensional monomial ideal, and ∆(I) be the simplicial complex whose Stanley–Reisner ideal is the polarization of I. It follows from a result of Soleyman Jahan that ∆(I) is shellable. We give a new short proof of this fact by providing an explicit shelling. Moreover, we show that ∆(I) is even vertex decomposable. The ideal L(I), which is defined to be the Sta...

In 1988 Kalai construct a large class of simplicial spheres, called squeezed spheres, and in 1991 presented a conjecture about generic initial ideals of Stanley–Reisner ideals of squeezed spheres. In the present paper this conjecture will be proved. In order to prove Kalai’s conjecture, based on the fact that every squeezed (d−1)-sphere is the boundary of a certain d-ball, called a squeezed d-b...

We consider stratifications of schemes by subvarieties, and introduce the notion of a stratification generated by a collection of (reduced) subschemes. We recall some basics of Gröbner degenerations (just for lex order) and Stanley-Reisner theory. We then state the main theorem, that the lex init of a Kazhdan-Lusztig variety in BottSamelson coördinates is the Stanley-Reisner scheme of a subword...

We develop an algebraic theory of supports for \(R\)-linear codes fixed length, where \(R\) is a finite commutative unitary ring. A support naturally induces notion generalized weights and allows one to associate monomial ideal code. Our main result states that, under suitable assumptions, the code can be obtained from graded Betti numbers its associated ideal. In case \(\mathbb{F}_q\)-linear e...