TY - JOUR
T1 - Betti numbers of toric ideals of graphs: A case study
AU - Galetto, Federico
AU - Hofscheier, Johannes
AU - Keiper, Graham
AU - Kohne, Craig
AU - Van Tuyl, Adam
AU - Paczka, Miguel Eduardo Uribe
PY - 2019/12/1
Y1 - 2019/12/1
N2 - 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 h-vector for all the toric ideals of graphs in this family.
AB - 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 h-vector for all the toric ideals of graphs in this family.
KW - Gröbner bases
KW - Hilbert series
KW - Toric ideals
KW - graded Betti numbers
KW - graphs
UR - https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85061709951&origin=inward
UR - https://www.scopus.com/inward/citedby.uri?partnerID=HzOxMe3b&scp=85061709951&origin=inward
U2 - 10.1142/S0219498819502268
DO - 10.1142/S0219498819502268
M3 - Article
SN - 0219-4988
VL - 18
JO - Journal of Algebra and its Applications
JF - Journal of Algebra and its Applications
IS - 12
M1 - 1950226
ER -