On the Characterization of<i>f</i>-Ideals

Anwar, Imran; Mahmood, Hasan; Binyamin, Muhammad Ahsan; Zafar, M. Khurram

doi:10.1080/00927872.2013.792092

Cited by 14 publications

(21 citation statements)

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“…In [1], the authors characterized the f -ideals of degree 2. This result was then generalized for unmixed f -ideals for degree d ≥ 2 in [2]. Later on the notion of f -graph was introduced in [9].…”

Section: Introductionmentioning

confidence: 98%

On the connectedness of f-simplicial complexes

et al. 2017

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In this paper, we introduce the concept of [Formula: see text]-simplicial complexes by generalizing the term of [Formula: see text]-graphs (introduced in [H. Mahmood, I. Anwar and M. K. Zafar, Construction of Cohen–Macaualy [Formula: see text]-graphs, J. Algebra Appl. 13(6) (2014) 1450012]). In particular, we discuss the problem of connectedness of pure [Formula: see text]-simplicial complexes. Moreover, we give a complete characterization of connected and disconnected [Formula: see text]-graphs and give a classification of all the disconnected [Formula: see text]-graphs.

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Section: Introductionmentioning

confidence: 98%

On the connectedness of f-simplicial complexes

et al. 2017

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“…In order to characterize f -ideals for any degree, it was needed to see it through combinatorial and topological aspects too. The characterization of f -ideals for homogeneous unmixed square-free monomial ideals of any degree d was given in [2], in which combinatorial aspects were also considered. Later on, the notion of f -graphs (in [13]) and f -simplicial complex (in [14]) was introduced.…”

Section: Introductionmentioning

confidence: 99%

“…Later on, the notion of f -graphs (in [13]) and f -simplicial complex (in [14]) was introduced. These notions have been studied for it various properties in the papers [1], [2], [5], [10], [11], [12], [13], [14] and [15]. In Computational Algebraic Geometry and Commutative Algebra, the notion of Hilbert polynomial and Hilbert series are very useful and important invariants of any finitely generated standard graded algebra over some field.…”

Section: Introductionmentioning

confidence: 99%

Quasi f-Ideals

Mahmood,

Rehman,

Nguyen

et al. 2020

Preprint

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The notion of f -ideals is recent and has been studied in the papers [14] and [15]. In this paper, we have generalized the idea of f -ideals to quasi f -ideals. This extended class of ideals is much bigger than the class of all f -ideals. Apart from giving various characterizations of quasi f -ideals of degree 2, we have determined all the minimal primes ideals of these ideals. Moreover, construction of quasi f -ideals of degree 2 has been described; the formula for computing Hilbert function and Hilbert series of the polynomial ring modulo quasi f -ideal has been provided.

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“…By Lemma 3.1 and the equation (1.1) in Section 1, (1) is clear. In order to prove (2), it will suffice to show that there exists a perfect set with cardinality t = n−d+2 i=5…”

Section: Correspondinglymentioning

confidence: 99%

“…The formal definition of an f -ideal appeared first in [1], and it is then studied in [2]. In [7], a monomial ideal I of K[x 1 , .…”

Section: Introductionmentioning

confidence: 99%

ON THE (n, d)^thf-IDEALS

Guo¹,

Wu²

2015

Journal of the Korean Mathematical Society

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Abstract. For a field K, a square-free monomial ideal I of K[x 1 , . . . , xn] is called an f -ideal, if both its facet complex and Stanley-Reisner complex have the same f -vector. Furthermore, for an f -ideal I, if all monomials in the minimal generating set G(I) have the same degree d, then I is called an (n, d) th f -ideal. In this paper, we prove the existence of (n, d) th f -ideal for d ≥ 2 and n ≥ d + 2, and we also give some algorithms to construct (n, d) th f -ideals.

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On the Characterization off-Ideals

Cited by 14 publications

References 3 publications

On the connectedness of f-simplicial complexes

On the connectedness of f-simplicial complexes

Quasi f-Ideals

ON THE (n, d)^thf-IDEALS

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On the Characterization off-Ideals

Cited by 14 publications

References 3 publications

On the connectedness of f-simplicial complexes

On the connectedness of f-simplicial complexes

Quasi f-Ideals

ON THE (n, d)thf-IDEALS

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ON THE (n, d)^thf-IDEALS