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### A broken circuit ring.

Beiträge zur Algebra und Geometrie

### A survey on local cohomology and 𝓓-modules

Banach Center Publications

### Algebraic properties of edge ideals via combinatorial topology.

The Electronic Journal of Combinatorics [electronic only]

### Betti numbers of monomial ideals and shifted skew shapes.

The Electronic Journal of Combinatorics [electronic only]

### Depth and Stanley depth of the facet ideals of some classes of simplicial complexes

Czechoslovak Mathematical Journal

Let ${\Delta }_{n,d}$ (resp. ${\Delta }_{n,d}^{\text{'}}$) be the simplicial complex and the facet ideal ${I}_{n,d}=\left({x}_{1}\cdots {x}_{d},{x}_{d-k+1}\cdots {x}_{2d-k},...,{x}_{n-d+1}\cdots {x}_{n}\right)$ (resp. ${J}_{n,d}=\left({x}_{1}\cdots {x}_{d},{x}_{d-k+1}\cdots {x}_{2d-k},...,{x}_{n-2d+2k+1}\cdots {x}_{n-d+2k},{x}_{n-d+k+1}\cdots {x}_{n}{x}_{1}\cdots {x}_{k}\right)$). When $d\ge 2k+1$, we give the exact formulas to compute the depth and Stanley depth of quotient rings $S/{J}_{n,d}$ and $S/{I}_{n,d}^{t}$ for all $t\ge 1$. When $d=2k$, we compute the depth and Stanley depth of quotient rings $S/{J}_{n,d}$ and $S/{I}_{n,d}$, and give lower bounds for the depth and Stanley depth of quotient rings $S/{I}_{n,d}^{t}$ for all $t\ge 1$.

### Dumont's statistic on words.

The Electronic Journal of Combinatorics [electronic only]

### Ehrhart clutters: regularity and max-flow min-cut.

The Electronic Journal of Combinatorics [electronic only]

### Face numbers and nongeneric initial ideals.

The Electronic Journal of Combinatorics [electronic only]

### Face vectors of two-dimensional Buchsbaum complexes.

The Electronic Journal of Combinatorics [electronic only]

### Failure of splitting from module-finite extension rings.

Beiträge zur Algebra und Geometrie

### Finite simplicial multicomplexes.

Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică

### Free minimal resolutions and the Betti numbers of the suspension of an $n$-gon.

International Journal of Mathematics and Mathematical Sciences

### Interpretations of the $h$-vector.

Boletín de la Asociación Matemática Venezolana

### Monomial ideals with 3-linear resolutions

Annales de la faculté des sciences de Toulouse Mathématiques

In this paper, we study the Castelnuovo-Mumford regularity of square-free monomial ideals generated in degree $3$. We define some operations on the clutters associated to such ideals and prove that the regularity is preserved under these operations. We apply these operations to introduce some classes of ideals with linear resolutions and also show that any clutter corresponding to a triangulation of the sphere does not have linear resolution while any proper subclutter of it has a linear resolution....

### On a theorem of Fröberg and saturated graphs.

Revista Colombiana de Matemáticas

### On Stanley-Reisner rings of reduction number one

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

### Shellability and the strong gcd-condition.

The Electronic Journal of Combinatorics [electronic only]

### Sign-graded posets, unimodality of $W$-polynomials and the Charney-Davis conjecture.

The Electronic Journal of Combinatorics [electronic only]

### Stanley decompositions and polarization

Czechoslovak Mathematical Journal

We define nice partitions of the multicomplex associated with a Stanley ideal. As the main result we show that if the monomial ideal $I$ is a CM Stanley ideal, then ${I}^{p}$ is a Stanley ideal as well, where ${I}^{p}$ is the polarization of $I$.

### Stanley filtrations and strongly stable ideals.

Beiträge zur Algebra und Geometrie

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