ROOTED ORDER ON MINIMAL GENERATORS OF POWERS OF SOME COVER IDEALS

Nursel, Erey

doi:https://doi.org/10.18910/87478

ROOTED ORDER ON MINIMAL GENERATORS OF POWERS OF SOME COVER IDEALS

Nursel, Erey

Osaka Journal of Mathematics, 2022, 59(2), 253-267

アクセス数:88件（2025-03-14 17:55 集計）

固定URL: https://doi.org/10.18910/87478

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タイトル	ROOTED ORDER ON MINIMAL GENERATORS OF POWERS OF SOME COVER IDEALS
著者	著者名 Nursel, Erey
抄録	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.
出版者	Osaka University and Osaka City University, Departments of Mathematics
収録物名	Osaka Journal of Mathematics
巻(号)	59(2)
ページ	253-267
刊行年月	2022-04
言語	英語
ハンドルURL	https://hdl.handle.net/11094/87478
DOI	https://doi.org/10.18910/87478
PISSN	00306126
NCID	AA00765910
アクセス権	open access
出版タイプ	Version of Record
カテゴリ	紀要論文 Departmental Bulletin Paper
カテゴリ	Osaka Journal of Mathematics / Volume 59, Number 2 （2022-4）

資源タイプ	紀要論文
ローカル資源タイプ	紀要論文
DCMI資源タイプ	text
DCTERMS.bibliographicCitation	Osaka Journal of Mathematics. 2022, 59(2), p. 253-267
DC.title	ROOTED ORDER ON MINIMAL GENERATORS OF POWERS OF SOME COVER IDEALS
DC.creator	Nursel, Erey
DC.publisher	Osaka University and Osaka City University, Departments of Mathematics
DC.language' scheme='DCTERMS.RFC1766	英語
DC.type' scheme='DCTERMS.DCMIType	text
DCTERMS.issued' scheme='DCTERMS.W3CDTF	2022-04
DCTERMS.abstract	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.
DC.identifier	10.18910/87478
DC.format	87478
citation_title	ROOTED ORDER ON MINIMAL GENERATORS OF POWERS OF SOME COVER IDEALS
citation_author	Nursel, Erey
citation_publisher	Osaka University and Osaka City University, Departments of Mathematics
citation_language	英語
citation_date	2022-04
citation_journal_title	Osaka Journal of Mathematics
citation_volume	59
citation_issue	2
citation_firstpage	253
citation_lastpage	267
citation_public_url	https://hdl.handle.net/11094/87478
citation_doi_detail	10.18910/87478
citation_doi	https://doi.org/10.18910/87478

ROOTED ORDER ON MINIMAL GENERATORS OF POWERS OF SOME COVER IDEALS

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