Gorenstein and Sr path ideals of cycles

Dariush Kiani, Sara Seedi Madani, Naoki Terai

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1 Citation (Scopus)


Let R = k[x 1,..,x n], where k is a field. The path ideal (of length t ≥ 2) of a directed graph G is the monomial ideal, denoted by It(G), whose generators correspond to the directed paths of length t in G. Let Cn be an n-cycle. We show that R/It(Cn) is Sr if and only if it is Cohen-Macaulay or n n-t-1 r+3. In addition, we prove that R/It(Cn) is Gorenstein if and only if n = t or 2t + 1. Also, we determine all ordinary and symbolic powers of It(Cn) which are Cohen-Macaulay. Finally, we prove that It(Cn) has a linear resolution if and only if t ≥ n-2.

Original languageEnglish
Pages (from-to)7-15
Number of pages9
JournalGlasgow Mathematical Journal
Issue number1
Publication statusPublished - Jan 25 2015
Externally publishedYes


  • 05C38
  • 05C75
  • 13F55
  • 2010 Mathematics Subject Classification 13D02

ASJC Scopus subject areas

  • Mathematics(all)


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