scholarly journals The Hilbert Series of the Face Ring of a Flag Complex

2002 ◽  
Vol 18 (3) ◽  
pp. 605-619 ◽  
Author(s):  
Paul Renteln
Keyword(s):  
Hilbert Series ◽  
Face Ring ◽  
Flag Complex ◽  
The Face

scholarly journals On algebraic characterization of SSC of the Jahangir’s graph 𝓙n,m

2018 ◽  
Vol 16 (1) ◽  
pp. 250-259
Author(s):  
Zahid Raza ◽  
Agha Kashif ◽  
Imran Anwar
Keyword(s):  
Simplicial Complex ◽  
Hilbert Series ◽  
Current Work ◽  
Algebraic Characterization ◽  
Face Ring ◽  
The Face

AbstractIn this paper, some algebraic and combinatorial characterizations of the spanning simplicial complex Δs(𝓙n,m) of the Jahangir’s graph 𝓙n,m are explored. We show that Δs(𝓙n,m) is pure, present the formula for f-vectors associated to it and hence deduce a recipe for computing the Hilbert series of the Face ring k[Δs(𝓙n,m)]. Finally, we show that the face ring of Δs(𝓙n,m) is Cohen-Macaulay and give some open scopes of the current work.

scholarly journals Effects of Elevated Atmospheric CO2 on Soil Microbial Biomass, Activity, and Diversity in a Chaparral Ecosystem

2005 ◽  
Vol 71 (12) ◽  
pp. 8573-8580 ◽  
Author(s):  
David A. Lipson ◽  
Richard F. Wilson ◽  
Walter C. Oechel
Keyword(s):  
Microbial Biomass ◽  
Enzymatic Activity ◽  
Fungal Biomass ◽  
Analysis Of Covariance ◽  
Root Production ◽  
Microbial Biomass C ◽  
Face Ring ◽  
Elevated Atmospheric Co2 ◽  
The Face ◽  
Biomass Activity

ABSTRACT This study reports the effects of long-term elevated atmospheric CO2 on root production and microbial activity, biomass, and diversity in a chaparral ecosystem in southern California. The free air CO2 enrichment (FACE) ring was located in a stand dominated by the woody shrub Adenostoma fasciculatum. Between 1995 and 2003, the FACE ring maintained an average daytime atmospheric CO2 concentration of 550 ppm. During the last two years of operation, observations were made on soil cores collected from the FACE ring and adjacent areas of chaparral with ambient CO2 levels. Root biomass roughly doubled in the FACE plot. Microbial biomass and activity were related to soil organic matter (OM) content, and so analysis of covariance was used to detect CO2 effects while controlling for variation across the landscape. Extracellular enzymatic activity (cellulase and amylase) and microbial biomass C (chloroform fumigation-extraction) increased more rapidly with OM in the FACE plot than in controls, but glucose substrate-induced respiration (SIR) rates did not. The metabolic quotient (field respiration over potential respiration) was significantly higher in FACE samples, possibly indicating that microbial respiration was less C limited under high CO2. The treatments also differed in the ratio of SIR to microbial biomass C, indicating a metabolic difference between the microbial communities. Bacterial diversity, described by 16S rRNA clone libraries, was unaffected by the CO2 treatment, but fungal biomass was stimulated. Furthermore, fungal biomass was correlated with cellulase and amylase activities, indicating that fungi were responsible for the stimulation of enzymatic activity in the FACE treatment.

scholarly journals Gorenstein rings through face rings of manifolds

2009 ◽  
Vol 145 (4) ◽  
pp. 993-1000 ◽  
Author(s):  
Isabella Novik ◽  
Ed Swartz
Keyword(s):  
Gorenstein Rings ◽  
Face Ring ◽  
Codimension Two ◽  
Homology Manifold ◽  
The Face ◽  
Homology Manifolds ◽  
System Of Parameters ◽  
Special Case ◽  
Generic System

AbstractThe face ring of a homology manifold (without boundary) modulo a generic system of parameters is studied. Its socle is computed and it is verified that a particular quotient of this ring is Gorenstein. This fact is used to prove that the algebraic g-conjecture for spheres implies all enumerative consequences of its far-reaching generalization (due to Kalai) to manifolds. A special case of Kalai’s conjecture is established for homology manifolds that have a codimension-two face whose link contains many vertices.

scholarly journals Face numbers of pseudomanifolds with isolated singularities

2012 ◽  
Vol 110 (2) ◽  
pp. 198 ◽  
Author(s):  
Isabella Novik ◽  
Ed Swartz
Keyword(s):  
Simplicial Complex ◽  
Upper Bound ◽  
Hilbert Function ◽  
Simplicial Complexes ◽  
Topological Invariant ◽  
Two Dimensional ◽  
Isolated Singularities ◽  
Face Ring ◽  
The Face

We investigate the face numbers of simplicial complexes with Buchsbaum vertex links, especially pseudomanifolds with isolated singularities. This includes deriving Dehn-Sommerville relations for pseudomanifolds with isolated singularities and establishing lower and upper bound theorems when the singularities are also homologically isolated. We give formulas for the Hilbert function of a generic Artinian reduction of the face ring when the singularities are homologically isolated and for any pure two-dimensional complex. Some examples of spaces where the $f$-vector can be completely characterized are described. We also show that the Hilbert function of a generic Artinian reduction of the face ring of a simplicial complex $\Delta$ with isolated singularities minus the $h$-vector of $\Delta$ is a PL-topological invariant.

scholarly journals Generalized Hilbert-Kunz function of the Rees algebra of the face ring of a simplicial complex

2021 ◽  
pp. 207-224
Author(s):  
Arindam Banerjee ◽  
Kriti Goel ◽  
J. Verma
Keyword(s):  
Simplicial Complex ◽  
Rees Algebra ◽  
Homogeneous Ideal ◽  
Content Type ◽  
Face Ring ◽  
The Face ◽  
S Period

Let R R be the face ring of a simplicial complex of dimension d − 1 d-1 and R ( n ) {\mathcal R}({\mathfrak {n}}) be the Rees algebra of the maximal homogeneous ideal n {\mathfrak {n}} of R . R. We show that the generalized Hilbert-Kunz function H K ( s ) = ℓ ( R ( n ) / ( n , n t ) [ s ] ) HK(s)=\ell ({\mathcal {R}}({\mathfrak {n}})/({\mathfrak {n}}, {\mathfrak {n}} t)^{[s]}) is given by a polynomial for all large s . s. We calculate it in many examples and also provide a Macaulay2 code for computing H K ( s ) . HK(s).

A dinucleating bis(dimethylcyclam) ligand and its dinickel(II) and dizinc(II) complexes with the face-to-face ring arrangement

1993 ◽  
Vol 32 (23) ◽  
pp. 4990-4991 ◽  
Author(s):  
Takashi Kajiwara ◽  
Tadashi Yamaguchi ◽  
Hiroaki Kido ◽  
Satoshi Kawabata ◽  
Reiko Kuroda ◽  
...  
Keyword(s):  
Face Ring ◽  
Face To Face ◽  
The Face

scholarly journals $k$-shellable simplicial complexes and graphs

2018 ◽  
Vol 122 (2) ◽  
pp. 161
Author(s):  
Rahim Rahmati-Asghar
Keyword(s):  
Simplicial Complex ◽  
Large Class ◽  
Simplicial Complexes ◽  
Face Ring ◽  
Stanley Conjecture ◽  
The Face ◽  
Shellable Simplicial Complex

In this paper we show that a $k$-shellable simplicial complex is the expansion of a shellable complex. We prove that the face ring of a pure $k$-shellable simplicial complex satisfies the Stanley conjecture. In this way, by applying an expansion functor to the face ring of a given pure shellable complex, we construct a large class of rings satisfying the Stanley conjecture.Also, by presenting some characterizations of $k$-shellable graphs, we extend some results due to Castrillón-Cruz, Cruz-Estrada and Van Tuyl-Villareal.

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