## 110 Citations

### Free Resolutions of Simplicial Posets

- Mathematics
- 1997

Abstract A simplicial poset, a poset with a minimal element and whose every interval is a Boolean algebra, is a generalization of a simplicial complex. Stanley defined a ring A P associated with a…

### A Survey of Eulerian Posets

- Mathematics
- 1994

An Eulerian poset is a finite graded poset with o and i such that every interval of length at least one has the same number of elements of odd rank as of even rank. For instance, the face lattice of…

### f-vectors of simplicial posets that are balls

- Mathematics
- 2010

Results of R. Stanley and M. Masuda completely characterize the h-vectors of simplicial posets whose order complexes are spheres. In this paper we examine the corresponding question in the case where…

### On q–simplicial posets

- Mathematics
- 2010

Much study of simplicial complexes and the more general simplicial posets has been undertaken. In this thesis we introduce q-analogues (q a prime power) of these two familiar objects, called…

### Moment-angle complexes from simplicial posets

- Mathematics
- 2009

We extend the construction of moment-angle complexes to simplicial posets by associating a certain Tm-space ZS to an arbitrary simplicial poset S on m vertices. Face rings ℤ[S] of simplicial posets…

### Stanley–Reisner rings for symmetric simplicial complexes, $G$-semimatroids and Abelian arrangements

- MathematicsJournal of Combinatorial Algebra
- 2021

We extend the notion of face rings of simplicial complexes and simplicial posets to the case of finite-length simplicial posets with a group action. The action on the complex induces an action on the…

### TORUS MANIFOLDS AND FACE RINGS OF BUCHSBAUM POSETS (New topics of transformation groups)

- Mathematics
- 2015

The paper aims to review the structure of the cohomology, equivariant cohomology, and the spectral sequence of the orbit type filtration of manifolds with locally standard torus actions. Certain…

### Simplicial chromatic polynomials as Hilbert series of Stanley--Reisner rings

- Mathematics
- 2022

We ﬁnd families of simplicial complexes where the simplicial chromatic polynomials deﬁned by Cooper–de Silva–Sazdanovic [5] are Hilbert series of Stanley– Reisner rings of auxiliary simplicial…

### Polyhedral products over finite posets

- MathematicsKyoto Journal of Mathematics
- 2022

Polyhedral products were defined by Bahri, Bendersky, Cohen and Gitler, to be spaces obtained as unions of certain product spaces indexed by the simplices of an abstract simplicial complex. In this…

### Title TORUS MANIFOLDS AND FACE RINGS OF BUCHSBAUM POSETS (New topics of transformation

- Mathematics
- 2020

The paper aims to review the structure of the cohomology, equivariant cohomology, and the spectral sequence of the orbit type filtration of manifolds with locally standard torus actions. Certain…

## References

SHOWING 1-10 OF 21 REFERENCES

### Cohen-Macaulay Complexes

- Mathematics
- 1977

Let Δ be a finite simplicial complex (or complex for short) on the vertex set V = (x1,…,xn). Thus, Δ is a collection of subsets of V satisfying the two conditions: (i) (xi) e Δ for all xi e V, and…

### The number of faces of balanced Cohen-Macaulay complexes and a generalized Macaulay theorem

- MathematicsComb.
- 1987

This work gives a characterization of thef-vectorsf=(fb)0≦b≦a′ or equivalently theh-vector, which can arise in this way from balanced Cohen-Macaulay complexes, and establishes a generalization of Macaulay’s compression theorem to colored multicomplexes.

### Combinatorics and commutative algebra

- Mathematics
- 1983

This text offers an overview of two of the main topics in the connections between commutative algebra and combinatorics. The first concerns the solutions of linear equations in non-negative integers.…

### An Introduction to Cohen-Macaulay Partially Ordered Sets

- Mathematics
- 1982

Combinatorics, algebra and topology come together in a most remarkable way in the theory of Cohen-Macaulay posets. These lectures will provide an introduction to the subject based on the work of…

### Distributive Lattices, Affine Semigroup Rings and Algebras with Straightening Laws

- Mathematics
- 1987

Summary. A lattice L is called integral over a field k if there exists a homogeneous ASL (algebra with straightening laws) domain on Lover k. By virtue of fundamental structure theorem of Birkhoff,…

### Commutative Ring Theory

- Mathematics
- 1989

Preface Introduction Conventions and terminology 1. Commutative rings and modules 2. prime ideals 3. Properties of extension rings 4. Valuation rings 5. Dimension theory 6. Regular sequences 7.…