Explicit Boij-Soderberg theory of ideals from a graph isomorphism reduction

Engström, Alexander; Jakobsson, Laura; Orlich, Milo

doi:10.48550/arxiv.1810.10055

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Booth-lueker Graphs2

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2020

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“…In this section we want to look at results relating to the edge ideal of the Booth-Lueker graph. In [7] the formulas for the Betti numbers and other invariants of the resolution were established in terms of the graph's number of edges and vertices. The cellularity of the resolution was not studied in this paper.…”

Section: Booth-lueker Graphsmentioning

confidence: 99%

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Families of cellular resolutions, their syzygies, and stability

Jakobsson

2020

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We study families of cellular resolutions by looking at them as a category and applying tools from representation stability. We obtain sufficient conditions on the structure of the family to have a noetherian representation category and apply this to concrete examples of families. In the study of syzygies we make use of defining the syzygy module as a representation and find conditions for the finite generation of this representation. We then show that many families of cellular resolutions coming from powers of ideals satisfy these conditions and have finitely generated syzygies, including the maximal ideals and edge ideals of paths.

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Section: Booth-lueker Graphsmentioning

confidence: 99%

“…The cellularity of the resolution was not studied in this paper. First we recall the Booth-Lueker edge ideal from [7] and some definitions from [4].…”

Section: Booth-lueker Graphsmentioning

confidence: 99%

Families of cellular resolutions, their syzygies, and stability

Jakobsson

2020

Preprint

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show abstract

Explicit Boij-Soderberg theory of ideals from a graph isomorphism reduction

Cited by 1 publication

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Families of cellular resolutions, their syzygies, and stability

Families of cellular resolutions, their syzygies, and stability

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