Constructing monomial ideals with a given minimal resolution

Sonja Mapes, Lindsay C. Piechnik

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


This paper gives a description of various recent results, which construct monomial ideals with a given minimal free resolution. We show that these results are all instances of coordinatizing a finite atomic lattice, as found in [11]. Subsequently, we explain how, in some of these cases [5, 6] where questions still remain, this point of view can be applied. We also prove an equivalence for trees between the notion of maximal defined in [6] and the notion of being maximal in a Betti stratum.

Original languageEnglish (US)
Pages (from-to)1963-1985
Number of pages23
JournalRocky Mountain Journal of Mathematics
Issue number6
StatePublished - 2017


  • Cellular resolution
  • Lcm-lattice
  • Minimal free resolution
  • Monomial ideal
  • Scarf ideal

ASJC Scopus subject areas

  • Mathematics(all)


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