Betti numbers of toric ideals of graphs: A case study Journal Articles

abstract

• We compute the graded Betti numbers for the toric ideal of a family of graphs constructed by adjoining a cycle to a complete bipartite graph. The key observation is that this family admits an initial ideal which has linear quotients. As a corollary, we compute the Hilbert series and [Formula: see text]-vector for all the toric ideals of graphs in this family.

authors

• Galetto, Federico
• Hofscheier, Johannes
• Keiper, Graham
• Kohne, Craig
• Van Tuyl, Adam
• Paczka, Miguel Eduardo Uribe

status

• published 

publication date

• December 2019

has subject area

• 0101 Pure Mathematics (FoR)

published in

• Journal of Algebra and its Applications  Journal

keywords

• ALGEBRAS
• DEPTH
• EDGE
• Grobner bases
• Hilbert series
• Mathematics
• Mathematics, Applied
• Physical Sciences
• RINGS
• Science & Technology
• Toric ideals
• graded Betti numbers
• graphs

Digital Object Identifier (DOI)

• 10.1142/s0219498819502268

start page

• 1950226

end page

• 1950226

volume

• 18

issue

• 12