リケラボ論文検索は、全国の大学リポジトリにある学位論文・教授論文を一括検索できる論文検索サービスです。

リケラボ 全国の大学リポジトリにある学位論文・教授論文を一括検索するならリケラボ論文検索大学・研究所にある論文を検索できる

リケラボ 全国の大学リポジトリにある学位論文・教授論文を一括検索するならリケラボ論文検索大学・研究所にある論文を検索できる

大学・研究所にある論文を検索できる 「ROOTED ORDER ON MINIMAL GENERATORS OF POWERS OF SOME COVER IDEALS」の論文概要。リケラボ論文検索は、全国の大学リポジトリにある学位論文・教授論文を一括検索できる論文検索サービスです。

コピーが完了しました

URLをコピーしました

論文の公開元へ論文の公開元へ
書き出し

ROOTED ORDER ON MINIMAL GENERATORS OF POWERS OF SOME COVER IDEALS

Nursel, Erey 大阪大学 DOI:10.18910/87478

2022.04

概要

We define a total order, which we call rooted order, on minimal generating set of J(Pn)s where J(Pn) is the cover ideal of a path graph on n vertices. We show that each power of a cover ideal of a path has linear quotients with respect to the rooted order. Along the way, we characterize minimal generating set of J(Pn)s for s ≥ 3 in terms of minimal generating set of J(Pn)2. We also discuss the extension of the concept of rooted order to chordal graphs. Computational examples suggest that such order gives linear quotients for powers of cover ideals of chordal graphs as well.

参考文献

[1] R. Abdolmaleki, J. Herzog and R. Zaare-Nahandi: On the initial behaviour of the number of generators of powers of monomial ideals, Bull. Math. Soc. Sci. Math. Roumanie 63 (111) (2020), 119–129.

[2] A. Constantinescu, M.R. Pournaki, S.A. Seyed Fakhari, N. Terai and S. Yassemi: Cohen-Macaulayness and limit behavior of depth for powers of cover ideals, Comm. Algebra 43 (2015), 143–157.

[3] B. Drabkin and L. Guerrieri: On quasi-equigenerated and Freiman cover ideals of graphs, Comm. Algebra 48 (2020), 4413–4435.

[4] S. Eliahou, J. Herzog and M. Mohammadi Saem: Monomial ideals with tiny squares, J. Algebra 514 (2018), 99–112.

[5] N. Erey: On the cover ideals of chordal graphs, Turkish J. Math. 43 (2019), 2405–2414.

[6] N. Erey and A.A. Qureshi: Second powers of cover ideals of paths, arXiv:1912.08161.

[7] S.A. Seyed Fakhari: Regularity of symbolic powers of cover ideals of graphs, Collect. Math. 70 (2019), 187–195.

[8] S.A. Seyed Fakhari: Symbolic powers of cover ideal of very well-covered and bipartite graphs, Proc. Amer. Math. Soc. 146 (2018), 97–110.

[9] C. Francisco and A. Van Tuyl: Sequentially Cohen-Macaulay edge ideals, Proc. Amer. Math. Soc. 135 (2007), 2327–2337.

[10] O. Gasanova: Monomial ideals with arbitrarily high tiny powers in any number of variables, Comm. Algebra 48 (2020), 4824–4831.

[11] I. Gitler, E. Reyes and R.H. Villarreal: Blowup algebras of ideals of vertex covers of bipartite graphs, in Algebraic structures and their representations, Contemp. Math. 376, Amer. Math. Soc., Providence, RI, 2005, 273–279.

[12] N.T. Hang and T.N. Trung: Regularity of powers of cover ideals of unimodular hypergraphs, J. Algebra 513 (2018), 159–176.

[13] J. Herzog and T. Hibi: Monomial Ideals, Springer-Verlag, London, 2011.

[14] J. Herzog, T. Hibi and S. Moradi: Componentwise linear powers and the x-condition, arXiv:2010.11516.

[15] J. Herzog, T. Hibi and H. Ohsugi: Powers of componentwise linear ideals; in Combinatorial Aspects of Commutative Algebra and Algebraic Geometry, Abel Symp., 6, Springer-Verlag, Berlin, 2011, 49–60.

[16] J. Herzog, M.M. Saem and N. Zamani: The number of generators of the powers of an ideal, Internat. J. Algebra Comput. 29 (2019), 827–847.

[17] J. Herzog and G. Zhu: Freiman ideals, Comm. Algebra 47 (2019), 407–423.

[18] V. Kodiyalam: Homological invariants of powers of an ideal, Proc. Amer. Math. Soc. 118 (1993), 757–764.

[19] A. Kumar and R. Kumar: On the powers of vertex cover ideals, J. Pure Appl. Algebra 226 (2022), Paper No.106808, 10pp.

[20] F. Mohammadi: Powers of the vertex cover ideal of a chordal graph, Comm. Algebra 39 (2011), 3753– 3764.

[21] F. Mohammadi: Powers of the vertex cover ideals, Collect. Math. 65 (2014), 169–181.

[22] A. Van Tuyl and R.H. Villarreal: Shellable graphs and sequentially Cohen-Macaulay bipartite graphs, J. Combin. Theory, Series A 115 (2008), 799–814.

[23] R. Woodroofe: Vertex decomposable graphs and obstructions to shellability, Proc. Amer. Math. Soc. 137 (2009), 3235–3246.

参考文献をもっと見る

全国の大学の
卒論・修論・学位論文

一発検索!

この論文の関連論文を見る