Depth and Stanley depth of the edge ideals of square paths and square cycles
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...
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| Format: | Article |
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Taylor and Francis Inc.
2018
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| _version_ | 1796863109915213824 |
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| author | Iqbal, Z. Ishaq, M. Aamir, M. |
| author_facet | Iqbal, Z. Ishaq, M. Aamir, M. |
| author_sort | Iqbal, Z. |
| collection | ePrints |
| description | 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. |
| first_indexed | 2024-03-05T20:21:47Z |
| format | Article |
| id | utm.eprints-79789 |
| institution | Universiti Teknologi Malaysia - ePrints |
| last_indexed | 2024-03-05T20:21:47Z |
| publishDate | 2018 |
| publisher | Taylor and Francis Inc. |
| record_format | dspace |
| spelling | utm.eprints-797892019-01-28T06:52:26Z http://eprints.utm.my/79789/ Depth and Stanley depth of the edge ideals of square paths and square cycles Iqbal, Z. Ishaq, M. Aamir, M. QA Mathematics 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. Taylor and Francis Inc. 2018 Article PeerReviewed 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 http://dx.doi.org/10.1080/00927872.2017.1339068 DOI:10.1080/00927872.2017.1339068 |
| spellingShingle | QA Mathematics Iqbal, Z. Ishaq, M. Aamir, M. Depth and Stanley depth of the edge ideals of square paths and square cycles |
| title | Depth and Stanley depth of the edge ideals of square paths and square cycles |
| title_full | Depth and Stanley depth of the edge ideals of square paths and square cycles |
| title_fullStr | Depth and Stanley depth of the edge ideals of square paths and square cycles |
| title_full_unstemmed | Depth and Stanley depth of the edge ideals of square paths and square cycles |
| title_short | Depth and Stanley depth of the edge ideals of square paths and square cycles |
| title_sort | depth and stanley depth of the edge ideals of square paths and square cycles |
| topic | QA Mathematics |
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