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

Iqbal, Z. and Ishaq, M. and Aamir, M. (2018) Depth and Stanley depth of the edge ideals of square paths and square cycles. Communications in Algebra, 46 (3). pp. 1188-1198. ISSN 0092-7872

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Official URL: http://dx.doi.org/10.1080/00927872.2017.1339068

Abstract

In this paper, we compute depth and Stanley depth for the quotient ring of the edge ideal associated to a square path on n vertices. We also compute depth and Stanley depth for the quotient ring of the edge ideal associated to a square cycle on n vertices, when n≡0,3,4(mod 5), and give tight bounds when n≡1,2(mod 5). We also prove a conjecture of Herzog presented in [5], for the edge ideals of square paths and square cycles.

Item Type:Article
Uncontrolled Keywords:Depth, edge ideal, monomial ideal, square cycle, square path, Stanley decomposition, Stanley depth
Subjects:Q Science > QA Mathematics
Divisions:Science
ID Code:79789
Deposited By: Fazli Masari
Deposited On:28 Jan 2019 06:52
Last Modified:28 Jan 2019 06:52

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