论文信息 - Depth and Stanley depth of the path ideal associated to an $n$-cyclic graph

Depth and Stanley depth of the path ideal associated to an $n$-cyclic graph

We compute the depth and Stanley depth for the quotient ring of the path ideal of length $3$ associated to a $n$-cyclic graph, given some precise formulas for depth when $n\not\equiv 1\,(\mbox{mod}\ 4)$, tight bounds when $n\equiv 1\,(\mbox{mod}\ 4)$ and for Stanley depth when $n\equiv 0,3\,(\mbox{mod}\ 4)$, tight bounds when $n\equiv 1,2\,(\mbox{mod}\ 4)$. Also, we give some formulas for depth and Stanley depth of a quotient of the path ideals of length $n-1$ and $n$.

Guangjun Zhu

[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] W. Vasconcelos. Arithmetic of Blowup Algebras , 1994 .

[4] Asia Rauf. STANLEY DECOMPOSITIONS, PRETTY CLEAN FILTRATIONS AND REDUCTIONS MODULO REGULAR ELEMENTS , 2007, 0708.1481.

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

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

[7] Susan Morey. Depths of Powers of the Edge Ideal of a Tree , 2009, 0908.0553.

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

[9] Jürgen Herzog,et al. A Survey on Stanley Depth , 2013 .

[10] Alin cStefan. Stanley depth of powers of the path ideal , 2014, 1409.6072.

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

[12] Mircea Cimpoeaş. Stanley depth of the path ideal associated to a line graph , 2015, 1508.07540.

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

[14] Guangjun Zhu. A lower bound for Stanley depth of squarefree monomial ideals , 2016 .