Properties of the Toric Rings of a Chordal Bipartite Family of Graphs

Ballard, Laura

doi:10.1007/978-3-030-91986-3_2

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2021

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Cited by 2 publications

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“…For more background, detail, and motivation, we refer the reader to [1], but note that different notation and indexing conventions have been employed in this work. Throughout, k is a field.…”

Section: Introductionmentioning

confidence: 99%

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Properties of the Toric Rings of a Chordal Bipartite Family of Graphs

Ballard¹

2021

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This work concerns the study of properties of a group of Koszul algebras coming from the toric ideals of a chordal bipartite infinite family of graphs (alternately, these rings may be interpreted as coming from determinants of certain ladder-like structures). We determine a linear system of parameters for each ring and explicitly determine the Hilbert series for the resulting Artinian reduction. As corollaries, we obtain the multiplicity and regularity of the original rings. This work extends results easily derived from lattice theory for a subfamily coming from a two-sided ladder to a family where, as we show, lattice theory no longer applies in any obvious way and includes constructive proofs which may be useful in future study of these rings and others.

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Section: Introductionmentioning

confidence: 99%

“…Macaulay2 [11] was used for computation and hypothesis formation. We would like to thank Syracuse University for its support and hospitality and Claudia Miller for her valuable input on the original project in [1] and this condensed version. We also acknowledge the partial support of an NSF grant.…”

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confidence: 99%