Abstract We describe the simplicial complex $$\Delta $$ Δ such that initial ideal of binomial edge $$J_\textrm{G}$$ J G G is Stanley-Reisner . By using we show if $$(S_2)$$ ( S 2 <mml:m...

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...

Abstract We study how some coefficients of two-variable coboundary polynomials can be derived from Betti numbers Stanley–Reisner rings. also explain the connection with these rings forces and Möbius to satisfy certain universal equations.

Let C ⊂ N be an affine semigroup, and R = K[C] its semigroup ring. This paper is a collection of various results on “C-graded” R-modules M = ⊕ c∈C Mc, especially, monomial ideals of R. For example, we show the following: If R is normal and I ⊂ R is a radicalmonomial ideal (i.e., R/I is a generalization of Stanley-Reisner rings), then the sequentially Cohen-Macaulay property of R/I is a topologi...

We answer positively a question of Asia Rauf for the case of intersections of three prime ideals generated by disjoint sets of variables and we present several inequalities on Stanley depth. This is a detailed presentation of our talk at the conference on ”Fundamental structures of algebra” in honor of Prof. Serban Basarab at his 70-th anniversary. Let S = K[x1, . . . , xn] be a polynomial alge...

A matroid complex is a pure complex such that every restriction is again pure. It is a long-standing open problem to classify all possible hvectors of such complexes. In the case when the complex has dimension 1 we completely resolve this question. We also prove the 1-dimensional case of a conjecture of Stanley that all matroid h-vectors are pure O-sequences. Finally, we completely characterize...