论文信息 - Stanley Depth of Edge Ideals of Some Wheel-Related Graphs

Stanley Depth of Edge Ideals of Some Wheel-Related Graphs

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.

Jia-bao Liu | M. Munir | Raheel Farooki | Muhammad Imran Qureshi | Quratulien Muneer

[1] Richard P. Stanley,et al. Linear diophantine equations and local cohomology , 1982 .

[2] J. Okninski,et al. On monomial algebras , 1988, Semigroup Algebras.

[3] Marius Vladoiu,et al. How to compute the Stanley depth of a monomial ideal , 2007, 0712.2308.

[4] Asia Rauf. Depth and Stanley Depth of Multigraded Modules , 2008, 0812.2080.

[5] G. Rinaldo. An algorithm to compute the Stanley depth of monomial ideals , 2009 .

[6] Mircea Cimpoeaş,et al. Stanley depth of monomial ideals with small number of generators , 2009, 0906.1105.

[7] M. I. Qureshi,et al. Computing the Stanley depth , 2009, 0907.0912.

[8] M. I. Qureshi,et al. ON THE BEHAVIOUR OF STANLEY DEPTH UNDER VARIABLE ADJUNCTION , 2010, 1007.3340.

[9] William T. Trotter,et al. Interval partitions and Stanley depth , 2010, J. Comb. Theory, Ser. A.

[10] M. I. Qureshi,et al. STANLEY DEPTH OF EDGE IDEALS , 2011, 1104.1018.

[11] M. I. Qureshi,et al. Upper and Lower Bounds for the Stanley Depth of Certain Classes of Monomial Ideals and Their Residue Class Rings , 2013 .

[12] Mircea Cimpoeaş. On the Stanley depth of edge ideals of line and cyclic graphs , 2014, 1411.0624.

[13] Art M. Duval,et al. A non-partitionable Cohen–Macaulay simplicial complex , 2015, Discrete Mathematics & Theoretical Computer Science.

[14] Zahid Iqbal,et al. Depth and Stanley depth of the edge ideals of square paths and square cycles , 2018 .