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 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).

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.

Spanning Simplicial Complex of Wheel Graph Wn

2019 ◽  
Vol 26 (02) ◽  
pp. 309-320 ◽  
Author(s):  
A. Zahid ◽  
M.U. Saleem ◽  
A. Kashif ◽  
M. Khan ◽  
M.A. Meraj ◽  
...  
Keyword(s):  
Simplicial Complex ◽  
Hilbert Series ◽  
Associated Primes ◽  
Face Ring ◽  
Combinatorial Properties ◽  
Ideal Formula ◽  
Wheel Graph ◽  
Vertex Set ◽  
Facet Ideal

In this paper, we explore the spanning simplicial complex of wheel graph Wn on vertex set [n]. Combinatorial properties of the spanning simplicial complex of wheel graph are discussed, which are then used to compute the f-vector and Hilbert series of face ring k[Δs(Wn)] for the spanning simplicial complex Δs(Wn). Moreover, the associated primes of the facet ideal [Formula: see text] are also computed.

The glycomes of Caenorhabditis elegans and other model organisms

2002 ◽  
Vol 69 ◽  
pp. 117-134 ◽  
Author(s):  
Stuart M. Haslam ◽  
David Gems ◽  
Howard R. Morris ◽  
Anne Dell
Keyword(s):  
Caenorhabditis Elegans ◽  
Current Knowledge ◽  
Structural Data ◽  
Model Organisms ◽  
Entire Genome ◽  
C Elegans ◽  
The Face ◽  
Area Of Concern ◽  
Nematode Worm

There is no doubt that the immense amount of information that is being generated by the initial sequencing and secondary interrogation of various genomes will change the face of glycobiological research. However, a major area of concern is that detailed structural knowledge of the ultimate products of genes that are identified as being involved in glycoconjugate biosynthesis is still limited. This is illustrated clearly by the nematode worm Caenorhabditis elegans, which was the first multicellular organism to have its entire genome sequenced. To date, only limited structural data on the glycosylated molecules of this organism have been reported. Our laboratory is addressing this problem by performing detailed MS structural characterization of the N-linked glycans of C. elegans; high-mannose structures dominate, with only minor amounts of complex-type structures. Novel, highly fucosylated truncated structures are also present which are difucosylated on the proximal N-acetylglucosamine of the chitobiose core as well as containing unusual Fucα1–2Gal1–2Man as peripheral structures. The implications of these results in terms of the identification of ligands for genomically predicted lectins and potential glycosyltransferases are discussed in this chapter. Current knowledge on the glycomes of other model organisms such as Dictyostelium discoideum, Saccharomyces cerevisiae and Drosophila melanogaster is also discussed briefly.

Exploring the Differences in Macrocognition Between Experts and Non-CHD Experts Managing Congenital Heart Disease (CHD)

2021 ◽  
Vol 10 (1) ◽  
pp. 335-339
Author(s):  
Azadeh Assadi ◽  
Peter C. Laussen ◽  
Patricia Trbovich
Keyword(s):  
Decision Making ◽  
Emergency Medicine ◽  
Congenital Heart Disease ◽  
Heart Disease ◽  
Congenital Heart ◽  
Pediatric Emergency ◽  
Acute Management ◽  
Naturalistic Decision Making ◽  
The Face

Background and aims: Children with congenital heart disease (CHD) are at risk of deterioration in the face of common childhood illnesses, and their resuscitation and acute management is often best achieved with the guidance of CHD experts. Access to such expertise may be limited outside specialty heart centers and the fragility of these patients is cause for discomfort among many emergency medicine physicians. An understanding of the differences in macrocognition of these clinicians could shed light on some of the causes of discomfort and facilitate the development of a sociotechnological solution to this problem. Methods: Cardiac intensivists (CHD experts) and pediatric emergency medicine physicians (non-CHD experts) in a major academic cardiac center were interviewed using the critical decision method. Interview transcripts were coded deductively based on Klein’s macrocognitive framework and inductively to allow for new or modified characterization of dimensions. Results: While both CHD-experts and non-CHD experts relied on the macrocognitive functions of sensemaking, naturalistic decision making and detecting problems, the specific data and mental models used to understand the patients and course of therapy differed between CHD-experts and non-CHD experts. Conclusion: Characterization of differences between the macrocognitive processes of CHD experts and non-CHD experts can inform development of sociotechnological solutions to augment decision making pertaining to the acute management of pediatric CHD patients.

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