scholarly journals On certain equidimensional polymatroidal ideals

2015 ◽  
Vol 149 (1-2) ◽  
pp. 223-233 ◽  
Author(s):  
Somayeh Bandari ◽  
Raheleh Jafari
Keyword(s):  
Polymatroidal Ideals

Weakly Polymatroidal Ideals

2006 ◽  
Vol 13 (04) ◽  
pp. 711-720 ◽  
Author(s):  
Masako Kokubo ◽  
Takayuki Hibi
Keyword(s):  
Betti Numbers ◽  
Partially Ordered Sets ◽  
Finite Sequence ◽  
Ordered Sets ◽  
Partially Ordered ◽  
Graded Betti Numbers ◽  
Linear Resolution ◽  
Fundamental Fact ◽  
Polymatroidal Ideals ◽  
Polymatroidal Ideal

The concept of the weakly polymatroidal ideal, which generalizes both the polymatroidal ideal and the prestable ideal, is introduced. A fundamental fact is that every weakly polymatroidal ideal has a linear resolution. One of the typical examples of weakly polymatroidal ideals arises from finite partially ordered sets. We associate each weakly polymatroidal ideal with a finite sequence, alled the polymatroidal sequence, which will be useful for the computation of graded Betti numbers of weakly polymatroidal ideals as well as for the construction of weakly polymatroidal ideals.

scholarly journals On stability properties of powers of polymatroidal ideals

2018 ◽  
Vol 70 (3) ◽  
pp. 357-365
Author(s):  
Shokoufe Karimi ◽  
Amir Mafi
Keyword(s):  
Stability Properties ◽  
Polymatroidal Ideals

scholarly journals The stable property of projective dimension

2019 ◽  
Vol 18 (12) ◽  
pp. 1950224
Author(s):  
Somayeh Bandari ◽  
Raheleh Jafari
Keyword(s):  
Projective Dimension ◽  
Monomial Ideals ◽  
Prime Ideals ◽  
Stable Property ◽  
Polymatroidal Ideals

We introduce the concept of monomial ideals with stable projective dimension, as a generalization of the Cohen–Macaulay property. Indeed, we study the class of monomial ideals [Formula: see text], whose projective dimension is stable under monomial localizations at monomial prime ideals [Formula: see text], with [Formula: see text]. We study the relations between this property and other sorts of Cohen–Macaulayness. Finally, we characterize some classes of polymatroidal ideals with stable projective dimension.

Stanley depth of factors of polymatroidal ideals and the edge ideal of forests

2015 ◽  
Vol 105 (4) ◽  
pp. 323-332 ◽  
Author(s):  
A. Alipour ◽  
S. A. Seyed Fakhari ◽  
S. Yassemi
Keyword(s):  
Edge Ideal ◽  
Stanley Depth ◽  
Polymatroidal Ideals

scholarly journals Monomial localizations and polymatroidal ideals

2013 ◽  
Vol 34 (4) ◽  
pp. 752-763 ◽  
Author(s):  
Somayeh Bandari ◽  
Jürgen Herzog
Keyword(s):  
Polymatroidal Ideals

On Standard Invariants of Bi-polymatroidal Ideals

2014 ◽  
Vol 21 (02) ◽  
pp. 267-274 ◽  
Author(s):  
Monica La Barbiera
Keyword(s):  
Polymatroidal Ideals

The standard invariants of the bi-polymatroidal ideals of Veronese type are computed.

scholarly journals Cohen–Macaulay polymatroidal ideals

2006 ◽  
Vol 27 (4) ◽  
pp. 513-517 ◽  
Author(s):  
Jürgen Herzog ◽  
Takayuki Hibi
Keyword(s):  
Polymatroidal Ideals

scholarly journals On the Stanley depth of weakly polymatroidal ideals

2013 ◽  
Vol 100 (2) ◽  
pp. 115-121 ◽  
Author(s):  
M. R. Pournaki ◽  
S. A. Seyed Fakhari ◽  
S. Yassemi
Keyword(s):  
Stanley Depth ◽  
Polymatroidal Ideals

scholarly journals Monomial Ideals with Primary Components given by Powers of Monomial Prime Ideals

10.37236/3813 ◽  
2014 ◽  
Vol 21 (1) ◽  
Author(s):  
Jürgen Herzog ◽  
Marius Vladoiu
Keyword(s):  
Monomial Ideals ◽  
Prime Ideals ◽  
Polymatroidal Ideals

We characterize monomial ideals which are intersections of powers of monomial prime ideals and study classes of ideals with this property, among them polymatroidal ideals.

scholarly journals Stanley depth of weakly polymatroidal ideals

2014 ◽  
Vol 103 (3) ◽  
pp. 229-233 ◽  
Author(s):  
S. A. Seyed Fakhari
Keyword(s):  
Stanley Depth ◽  
Polymatroidal Ideals
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