scholarly journals Values and bounds for depth and Stanley depth of some classes of edge ideals

2021 ◽  
Vol 6 (8) ◽  
pp. 8544-8566
Author(s):  
Naeem Ud Din ◽  
◽  
Muhammad Ishaq ◽  
Zunaira Sajid
Keyword(s):  
Stanley Depth ◽  
Edge Ideals

scholarly journals Stanley depth of edge ideals

2012 ◽  
Vol 49 (4) ◽  
pp. 501-508 ◽  
Author(s):  
Muhammad Ishaq ◽  
Muhammad Qureshi
Keyword(s):  
Complete Graph ◽  
Upper Bound ◽  
Edge Ideal ◽  
Stanley Depth ◽  
Edge Ideals

We give an upper bound for the Stanley depth of the edge ideal I of a k-partite complete graph and show that Stanley’s conjecture holds for I. Also we give an upper bound for the Stanley depth of the edge ideal of a s-uniform complete bipartite hypergraph.

scholarly journals Stanley Depth of Edge Ideals of Some Wheel-Related Graphs

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 202 ◽  
Author(s):  
Jia-Bao Liu ◽  
Mobeen Munir ◽  
Raheel Farooki ◽  
Muhammad Imran Qureshi ◽  
Quratulien Muneer
Keyword(s):  
Geometric Invariant ◽  
Stanley Depth ◽  
Edge Ideals ◽  
Algebraic Invariant ◽  
Wheel Graph

Stanley depth is a geometric invariant of the module and is related to an algebraic invariant called depth of the module. We compute Stanley depth of the quotient of edge ideals associated with some familiar families of wheel-related graphs. In particular, we establish general closed formulas for Stanley depth of quotient of edge ideals associated with the m t h -power of a wheel graph, for m ≥ 3 , gear graphs and anti-web gear graphs.

scholarly journals On the Stanley depth of powers of edge ideals

2017 ◽  
Vol 489 ◽  
pp. 463-474 ◽  
Author(s):  
S.A. Seyed Fakhari
Keyword(s):  
Stanley Depth ◽  
Edge Ideals

scholarly journals Depth and Stanley depth of the edge ideals of square paths and square cycles

2017 ◽  
Vol 46 (3) ◽  
pp. 1188-1198 ◽  
Author(s):  
Zahid Iqbal ◽  
Muhammad Ishaq ◽  
Muhammad Aamir
Keyword(s):  
Stanley Depth ◽  
Edge Ideals

scholarly journals Depth and Stanley depth of the edge ideals of the powers of paths and cycles

2019 ◽  
Vol 27 (3) ◽  
pp. 113-135
Author(s):  
Zahid Iqbal ◽  
Muhammad Ishaq
Keyword(s):  
Positive Integer ◽  
Lower Bounds ◽  
Quotient Ring ◽  
Edge Ideal ◽  
Stanley Depth ◽  
Edge Ideals

AbstractLet k be a positive integer. We compute depth and Stanley depth of the quotient ring of the edge ideal associated to the kth power of a path on n vertices. We show that both depth and Stanley depth have the same values and can be given in terms of k and n. If n≣0, k + 1, k + 2, . . . , 2k(mod(2k + 1)), then we give values of depth and Stanley depth of the quotient ring of the edge ideal associated to the kth power of a cycle on n vertices and tight bounds otherwise, in terms of n and k. We also compute lower bounds for the Stanley depth of the edge ideals associated to the kth power of a path and a cycle and prove a conjecture of Herzog for these ideals.

scholarly journals Depth and Stanley depth of edge ideals associated to some line graphs

2019 ◽  
Vol 4 (3) ◽  
pp. 686-698 ◽  
Author(s):  
Zahid Iqbal ◽  
◽  
Muhammad Ishaq
Keyword(s):  
Line Graphs ◽  
Stanley Depth ◽  
Edge Ideals

scholarly journals A proof for a conjecture on the regularity of binomial edge ideals

2021 ◽  
Vol 180 ◽  
pp. 105432
Author(s):  
Mohammad Rouzbahani Malayeri ◽  
Sara Saeedi Madani ◽  
Dariush Kiani
Keyword(s):  
Edge Ideals

On Stanley Depths of Certain Monomial Factor Algebras

2015 ◽  
Vol 58 (2) ◽  
pp. 393-401
Author(s):  
Zhongming Tang
Keyword(s):  
Polynomial Ring ◽  
Monomial Ideal ◽  
Primary Decomposition ◽  
Factor Algebra ◽  
Stanley Depth ◽  
Stanley Conjecture ◽  
Stanley Decomposition

AbstractLet S = K[x1 , . . . , xn] be the polynomial ring in n-variables over a ûeld K and I a monomial ideal of S. According to one standard primary decomposition of I, we get a Stanley decomposition of the monomial factor algebra S/I. Using this Stanley decomposition, one can estimate the Stanley depth of S/I. It is proved that sdepthS(S/I) ≤ sizeS(I). When I is squarefree and bigsizeS(I) ≤ 2, the Stanley conjecture holds for S/I, i.e., sdepthS(S/I) ≥ depthS(S/I).

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