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ON THE DEPTH OF SYMBOLIC POWERS OF EDGE IDEALS OF GRAPHS

Part of: Theory of modules and ideals Arithmetic rings and other special rings Algebraic combinatorics

Published online by Cambridge University Press:  28 September 2020

S. A. S. FAKHARI
S. A. S. FAKHARI*
Affiliation:
School of Mathematics, Statistics and Computer Science, College of Science University of TehranTehranIran
*
aminfakhari@ut.ac.ir
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Abstract

Assume that G is a graph with edge ideal $I(G)$ and star packing number $\alpha _2(G)$ . We denote the sth symbolic power of $I(G)$ by $I(G)^{(s)}$ . It is shown that the inequality $ \operatorname {\mathrm {depth}} S/(I(G)^{(s)})\geq \alpha _2(G)-s+1$ is true for every chordal graph G and every integer $s\geq 1$ . Moreover, it is proved that for any graph G, we have $ \operatorname {\mathrm {depth}} S/(I(G)^{(2)})\geq \alpha _2(G)-1$ .

MSC classification

Primary: 13C15: Dimension theory, depth, related rings (catenary, etc.) 13F55: Stanley-Reisner face rings; simplicial complexes 05E40: Combinatorial aspects of commutative algebra
Type
Article
Information
Nagoya Mathematical Journal , Volume 245 , March 2022 , pp. 28 - 40
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Copyright
© Foundation Nagoya Mathematical Journal, 2020

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